The Houston Texans signed Boswell on May 10, 2014 to compete with Randy Bullock. Boswell was cut on August 29. He was re-signed to the practice squad on September 23, 2014.

On January 7, 2015, Boswell signed a reserve/future contract with the New York Giants. On August 16, 2015, Boswell was waived by the Giants. On September 2, 2015, he was re-signed by the Giants. On September 5, 2015, Boswell was waived after failing to make the final 53-man roster.

Boswell signed with the Pittsburgh Steelers on October 3, 2015, becoming their fourth placekicker in 2015.

On September 18, Boswell kicked a season-long 49-yard field goal against the Cincinnati Bengals. On October 23, Boswell kicked three field goals but missed two against the New England Patriots. On November 20, Boswell kicked three field goals against the Cleveland Browns. On December 11, Boswell kicked two field goals against the Buffalo Bills. On December 18, Boswell kicked a career-high six field goals against the Cincinnati Bengals. He is the first kicker in NFL history to convert at least six field goals in a game and have five of those connect from 40+ yards. The last kicker to kick five field goals from 40+ yards in the same game was Mason Crosby in 2015. He is the third Pittsburgh Steeler in franchise history to accomplish the feat. (Jeff Reed in 2002 and Gary Anderson twice in 1988). On January 15, 2017, In the divisional playoff, he set a playoff record, kicking 6 field goals leading the team to beat the Kansas City Chiefs 18–16, scoring all of the Steelers’ points. Boswell’s four first-half field goals also tied the team record for an entire playoff game.

Boswell made his NFL debut on October 12, completing all three of his extra points and making a 47-yard field goal attempt in a Monday night victory over the San Diego Chargers. He connected on the longest debut conversion in team history, besting Todd Peterson’s record of 46. On October 18, the following week against the Arizona Cardinals, Boswell was 4-for-4 on field goals including kicks of 48, 49, and 51 yards, earning him AFC Special Teams Player of the Week honors. He is the first Steeler in team history to make three 47+ yard field goals in one game. On November 8, Boswell kicked three field goals, including the game-winner and three PATs against the Oakland Raiders., albeit missing his first field goal season-to-date. On November 15, Boswell kicked three field goals against the Cleveland Browns. His 14 field goals is tied for fourth among rookie/first-year players in team history, just behind Jeff Reed (2002, 17). On November 29, Boswell kicked three field goals against the Seattle Seahawks. On October 25, Boswell kicked two field goals against the Kansas City Chiefs. On December 6, Boswell kicked three field goals against the Indianapolis Colts. On December 13, Boswell kicked four field goals against the Cincinnati Bengals. On December 20, Boswell kicked two field goals against the Denver Broncos. He tied a franchise record for the most consecutive games played while scoring at least 10 points, tied with Gary Anderson (1985). He also passed Kris Brown for the most made field goals by a rookie or first-year player in the history of the franchise with 29. He also set Steelers’ records for rookie/first-year kickers for points in a season with 113 and field goal percentage at 90.6. On January 7, 2016, Boswell won AFC Special Teams Player of the Month for the month of December.

On January 9, 2016, Boswell kicked four field goals in an 18–16 win in the AFC Wild Card game against the Cincinnati Bengals. He successfully kicked a 35-yard game-winning field goal with less than 20 seconds remaining in the game. He set an NFL record for the most field goals by a rookie/first-year player in a playoff game. His four field goals also tied for the most in Steelers playoff history (Gary Anderson in the 1989 Wild Card Round). He also became the youngest kicker to make four field goals in a postseason game. On January 17, 2016, in a loss against the Denver Broncos during the Divisional Round of the playoffs, Boswell tied a franchise record with seven total field goals completed in the post-season.

On February 2, 2017, the Steelers signed Boswell to a one-year, exclusive-rights contract. In Week 2, against the Minnesota Vikings, Boswell converted four field goals and two extra points in the 26–9 victory. In Week 7, He kicked a season-high five field goals against the Cincinnati Bengals. In Week 11, he kicked four field goals in a 40-17 win against the Tennessee Titans. Boswell made a game-winning 53-yard field goal in Week 12 (November 26, 2017) to beat the Green Bay Packers 31-28 as time expired. His game-winner set a new career-long and tied kicker Dan Bailey’s record set in 2016 for the longest NFL field goal ever kicked at Heinz Field (53 yards) in its 17-year history. The only longer successful attempt was in collegiate play when former Old Dominion kicker Jarod Brown made a 54-yard kick against the Pitt Panthers in 2013. In Week 13, Boswell converted both extra points and all three field goal attempts, including a 38-yard game-winner as time expired, in a 23–20 comeback win over the Bengals, earning him AFC Special Teams Player of the Week. The next week he kicked four field goals including a game-winner against the Baltimore Ravens. Throughout the season, Boswell has kicked multiple game-winning field goals in the last minutes, earning him status as one of the Steelers’ “Killer B’s” and a spot on the AFC’s Pro Bowl starting roster. He finished the season tied with Harrison Butker for fourth in scoring with 142 points.

On March 12, 2018, the Steelers placed a second-round restricted free agent tender on Boswell. On April 5, he signed the tender. On August 23, 2018, the Steelers signed Boswell to a new five-year deal, keeping him under contract through the 2022 season. Boswell was later named a captain alongside Ben Roethlisberger, Maurkice Pouncey, and Cameron Heyward.

Boswell had a down year in 2018, converting only 13 of 20 field goal attempts and 43 of 48 extra point attempts. His 65% field goal percentage was ranked last among kickers with at least 20 field goal attempts.

He was placed on injured reserve on December 28, 2018. It was revealed that he suffered a grade-2 tear in his groin as reported by his brother, Stephen Boswell. Boswell was replaced by kicker Matt McCrane for the Steelers’ final game against the Cincinnati Bengals for the 2018 season.

Boswell rebounded in 2019, going 29 for 31 (93.5%) on field goal attempts and a perfect 28 for 28 on extra point attempts.

On November 8, 2020 in a game at AT&T Stadium against the Dallas Cowboys, Boswell made a career-long 59-yard field goal which also set the Steelers franchise record for longest field goal.