On July 2, 2009, the Tennessee Titans signed Cook to a four-year, $2.45 million contract that included a signing bonus of $711,000.

On September 20, 2009, he made his professional debut in the Titans’ Week 2 loss to the Houston Texans after being a healthy scratch the previous week. On October 4, 2009, Cook caught two passes for 11 yards during a 37–17 loss at the Jacksonville Jaguars in Week 4. Cook caught his first NFL reception from quarterback Kerry Collins for a five-yard gain in the third quarter. In Week 5, he made a season-high three receptions for 27 yards in the Titans’ 31–9 loss to the Indianapolis Colts.

The Tennessee Titans selected Cook in the third round (89th overall) of the 2009 NFL Draft. The Tennessee Titans traded their second round pick in the 2010 NFL Draft to the New England Patriots in order to draft Cook. Cook was the third tight end drafted in 2009.

Cook competed against Craig Stevens throughout training camp to be the second tight end on the depth chart after Alge Crumpler departed during free agency. Offensive coordinator Mike Heimerdinger named Cook the third tight end on the depth chart to start the season, behind Bo Scaife and Craig Stevens. On December 19, 2010, Cook earned his first career start after Bo Scaife was benched as a possible result of comments he made about a divided locker room. He finished the Titans 31–17 victory against the Houston Texans with three catches for 42 receiving yards. On December 26, 2010, Cook caught five passes for a season-high 96 yards and scored his first NFL touchdown during a 34–14 loss at the Kansas City Chiefs. He caught a 22-yard touchdown reception off a pass by quarterback Kerry Collins in the third quarter to mark his first career touchdown. In Week 17, he caught a season-high seven passes for 57 yards as the Titans lost 23–20 at the Indianapolis Colts.

Cook appeared in all 16 games and made one start in 2010 while making 29 receptions for 361 receiving yards and a touchdown. He also had a career-high six combined tackles on special teams.

On January 28, 2011, the Titans fired head coach Jeff Fisher after they finished fourth in the AFC South with a 6-10 record in 2010.

On October 2, 2011, Cook caught two passes for 93 yards and scored on an 80-yard touchdown reception from quarterback Matt Hasselbeck during a 31–13 win at the Cleveland Browns. In Week 15, he had a season-high nine catches for 103 yards as the Titans lost at the Indianapolis Colts by a score of 27–13. The following week, Cook caught eight passes for a season-high 169 yards and a touchdown during a 23–17 win at the Jacksonville Jaguars in Week 16. Cook caught a 55-yard touchdown pass from quarterback Matt Hasselbeck in the first quarter.

Cook appeared in all 16 games and had five starts in 2011 while catching 49 passes for a career-high 759 receiving yards and three touchdowns. He also made five solo tackles while appearing on special teams in 2011.

Cook returned as the secondary tight end behind Craig Stevens in 2012 under offensive coordinator Chris Palmer. In Week 3, Cook made four receptions for a season-high 77 yards and a touchdown in a 44–41 win against the Detroit Lions. On November 25, he caught a season-high six passes for 47 yards during a 24–19 loss at the Jacksonville Jaguars. On December 9, 2012, Cook caught three passes for 20 yards and a touchdown before exiting during a 27–23 loss at the Indianapolis Colts due to an injury.

On March 12, 2013, the St. Louis Rams signed Cook to a five-year, $35.10 million contract with $16 million guaranteed where he was reunited with Jeff Fisher.

During the offseason, Cook was expected to be cut by the St. Louis Rams due to his $8.30 million cap number in 2016. On February 19, 2016, the Rams officially released Cook, freeing $5.69 million in cap space. As an unrestricted free agent, Cook received interest from a few teams and attended a meeting with the Green Bay Packers.

On March 28, 2016, the Green Bay Packers signed Cook to a one-year, $2.75 million contract with $875,000 guaranteed.

On June 3, 2016, it was reported that Cook underwent surgery on his foot. The surgery was deemed a preventive measure and his recovery caused him to miss the majority of training camp. On August 9, 2016, Cook returned from his injury and fully participated in training camp. His absence significantly delayed his ability to become the primary tight end for the Green Bay Packers and he was subsequently named the secondary starting tight end to begin the regular season, behind Richard Rodgers.

On September 25, 2016, Cook caught a pass for a 15-yard gain before exiting in the second quarter of the Packers’ 34–27 victory against the Detroit Lions after spraining his ankle. Cook was subsequently inactive for the next six games (Weeks 4–10) due to the ankle injury. His injury ended his 51-game streak of consecutive game appearances. On November 20, Cook returned from his injury and caught a season-high six passes for 105 yards and a touchdown during a 42–24 loss at the Washington Redskins. During the fourth quarter, Cook caught a six-yard pass from quarterback Aaron Rodgers, but had it stripped away by cornerback Josh Norman. Cook finished his single season with the Packers with 30 receptions for 377 receiving yards and a touchdown in ten games and five starts. Cook received an overall grade of 81.0 from Pro Football Focus and ranked 11th among all qualified tight ends in 2016.

The Packers finished first in the NFC North with a 10–6 record and earned a playoff berth. On January 8, 2017, Cook appeared in his first career playoff game and caught five passes for 48 yards during a 38–13 win against the New York Giants in the NFC Wildcard Game. On January 15, 2017, Cook made six receptions for 103 yards and a touchdown as the Packers’ defeated the Dallas Cowboys 34–31 in the NFC Divisional Round. During the fourth quarter, Cook caught a 36-yard pass from Aaron Rodgers along the sideline with three seconds left to set up the Packers’ game-winning 51-yard field goal by Mason Crosby. The following week, Cook started in the NFC Championship Game and caught seven passes for 78 yards and a touchdown during a 44–21 loss at the Atlanta Falcons.

On March 16, 2017, the Oakland Raiders signed Cook to a two-year, $10.60 million contract with $5 million guaranteed.

Cook started in all 16 games for the first time in his career and made a then career-high 54 receptions for 688 receiving yards and two touchdowns. Additionally, he earned an overall grade of 52.8 from Pro Football Focus, which ranked 36th among all qualified tight ends in 2017.

On March 26, 2019, Cook signed a two-year contract worth $15.5 million with the New Orleans Saints.