In 1892, Tenney played his first professional game for the Binghamton Bingos of the Eastern League, going 1 for 4 with a single. He played as Brown University’s catcher for the 1893 and 1894 seasons. In 1894, the team had a 23–8 record and were selected as national champions by Harper’s Weekly. The night of his senior dinner, Tenney received a telephone message from Frank Selee, the manager of the Beaneaters, asking him to play a game for the team at catcher, due to the injuries of other players.

In his MLB debut on June 16, 1894, Tenney had to be removed from the game in the fifth inning due to a fractured finger on his throwing hand from a foul tip. After Tenney had his finger addressed, James Billings, an owner of the Beaneaters, offered him a contract worth US$300 a month from that day. Tenney, later writing about the day, stated:

Tenney married a Georgetown girl, Bessie Farnham Berry, on October 21, 1895. The couple had two children together; Barbara, born July 4, 1899, and Ruth, born December 8, 1901. Early in his career, he refused to play baseball on Sundays due to his religion, although he later changed his mind. Tenney was known as the “Soiled Collegian” at the major league level because it was unpopular for college players to become professional. Tenney served as a journalist for The Boston Post, Baseball Magazine, and The New York Times. He painted and sketched during the winter.

He returned to the team a month later, and finished the year batting .395 in 27 games. The following season, Tenney moved to the outfield due to an erratic throwing arm behind the plate, according to manager Selee. For the season, he hit .272 in 49 games, while also playing minor league baseball for the New Bedford Whalers. In 1896, Tenney again caught and played outfield; offensively, however, Tenney hit .336 in nearly double the games from the previous year (88) despite playing in the minors for the Springfield Ponies.

In 1897, Tenney moved to first base to replace the aging Tom Tucker. According to Alfred Henry Spink, within two weeks of the move it was evident that Tenney had become “one of the finest first sackers that the game [had] ever seen.” On June 14, 1897, in a game against the Cincinnati Reds, Tenney turned the first 3-6-3 double play in MLB history. Offensively, Tenney led MLB in plate appearances (646) and tied Duff Cooley, Gene DeMontreville, and George Van Haltren for the lead in at bats (566) as the Boston club became National League (NL) champions with a 93–39 record.

Boston again won the NL in 1898 while Tenney hit .328 with 62 RBIs. In 1899 he collected 209 hits, fifth most in MLB, and recorded 17 triples, good for fourth best in MLB. In 1900 Tenney, at age 28, batted .279 over 112 games played. He began a streak of seven consecutive seasons where he led the NL in assists in 1901; he holds the record for most seasons leading a league in assists, with eight, including one in 1899. He was suspended for ten games for fighting Pittsburgh Pirates manager Fred Clarke in May 1902, and finished the 1902 season with the second most sacrifice hits (29) in the majors, to go along with a .315 average. Throughout the 1901–1902 seasons, Tenney received contract offers worth up to $7,000 ($206,248 in 2017) from St. Louis, Cleveland, and Detroit; Tenney, however, decided to remain in Boston, and was named captain of the club in 1903. For the season, he hit .313, with 41 RBIs and three home runs, as he led his team in walks (70) and had the best on-base percentage mark (.415) on the squad. In 1904, Tenney again led his team in walks and on-base percentage, as he tied for the team lead in runs with Ed Abbaticchio.

He was named manager of the team in 1905, but did not receive additional pay; he was, however, offered a bonus if the team didn’t lose money. In 1905, Tenney tried to sign William Clarence Matthews, an African-American middle infielder from Harvard University, to a contract. Tenney later retracted his offer due to pressure from MLB players. Defensively, he led the majors in errors committed by a first baseman and finished second in most putouts for any position. Tenney led the 1906 Beaneaters to a 49–102 record. For the second straight year, the Boston team lost more than 100 games.

After a 158–295 record as manager, on December 3, 1907, Tenney was traded to the Giants, along with Al Bridwell and Tom Needham, for Frank Bowerman, George Browne, Bill Dahlen, Cecil Ferguson and Dan McGann; the trade was called “one of the biggest deals in the history of National League baseball”.

After batting a career low .235 in 1909, Tenney was released by the Giants. He spent the 1910 season as a player–manager for the minor league Lowell Tigers, leading the team to a 65–57 record, good for fourth (out of eight teams) in the New England League.

On December 19, 1910, Tenney signed a two-year contract with the Boston Rustlers. For the 1911 season, Tenney hit .263 over 102 games. He was released by the Braves on March 20, 1912, after 44–107 record in one season; Tenney was paid not to manage for the second year on his contract.

After retiring from baseball, Tenney worked for the Equitable Life Insurance Society and continued writing for The New York Times. In 1912, he was vice-president of the Usher–Stoughton shoe manufacturing company in Lynn, Massachusetts; later, he formed the Tenney–Spinney Shoe Company in partnership with Henry Spinney. He was balloted for the National Baseball Hall of Fame from 1936–1942 and again in 1946, but never received more than eight votes, receiving eight (3.1% of total ballots cast) during the Baseball Hall of Fame balloting in 1938. Tenney died on July 3, 1952 at Massachusetts General Hospital after a long illness. He was interred at Harmony Chapel and Cemetery in Georgetown.

In 1916, he bought the Newark Indians of the International League with James R. Price for $25,000 ($527,450 in 2012). Mayor Thomas Lynch Raymond declared April 27 a “half-holiday” for the city of Newark for the Indians’ Opening Day. Tenney played in 16 games for the Indians, hitting .318 with seven hits over 22 at-bats, and managed the team to a 52–87 record.