In 2012, Krug was named the CCHA Player of the Year, and was a finalist for the Hobey Baker Award.
A product of the Belle Tire midget program in Michigan, Krug skated in 59 regular season games for the Indiana Ice of the USHL, notching 47 points. He also skated in 13 Clark Cup playoff games with seven points before capturing the championship. He was a member of the USHL All-Rookie Team and set the Indiana Ice record for points in a season by a defenseman in 2008–09.
Krug arrived at Michigan State University in the Fall of 2009, and was initially slotted as a fifth or sixth defenseman on the roster. During the 2009–10 season, Krug was voted to the CCHA's All-Rookie Team. After skating in all 38 games, he finished the season second on the team in rookie scoring and led all CCHA first-year defensemen in scoring. Krug quickly gained a reputation as one of the CCHA’s most offensive performers, and in advance of his sophomore season, was elected captain of the Spartans. As a sophomore, Krug was named to the First Team All-CCHA, and was voted the CCHA's Top Offensive Defenseman (he was the CCHA's top-scoring defenseman that year). In 2011–12, he was named to the All-CCHA Team for the second time, and was named a CCHA Player of the Year and Hobey Baker Award finalist. During the season, he was the top scoring defenseman in the CCHA, and shared the CCHA conference scoring title with Notre Dame's T. J. Tynan (29 points), becoming the first defenseman in the league to win a scoring title since Western Michigan's Wayne Gagner in 1986–87.
For his accomplishments with Michigan State, Krug was among collegiate hockey's most sought-after free agents when he signed with the Boston Bruins in 2012.
On March 25, 2012, Krug was signed to an entry-level contract by the Boston Bruins, making his NHL debut on April 3, 2012, against the Pittsburgh Penguins. Appearing in two games with the Bruins, Krug finished with one assist and had an even plus-minus rating, averaging just over 17 minutes of ice time per game.
Krug spent the 2012–13 season with the Providence Bruins, where he was hampered by a sprained ankle until mid-January. After being called up from Providence on an emergency basis, he scored his first NHL goal during his first Stanley Cup playoff game in the Eastern Conference Semi-finals against the New York Rangers, becoming the first Bruins defenseman to score in his playoff debut since Glen Wesley in 1988. Krug followed this by scoring his second NHL goal during Game 2 of the same series, becoming the fourth player in Bruins history to score goals in his first two playoff games. At the conclusion of the series, he became the first rookie defenseman in League history to score four goals in his first five playoff games. In the 2013 postseason, Krug was a sensation, scoring 4 goals and recording 6 assists.
Krug started the 2013–14 season on the Bruins' opening night roster, and scored his first regular season NHL goal on October 5, 2013, against Jimmy Howard of the Detroit Red Wings. On November 25, playing against the Pittsburgh Penguins, he became the first rookie defenseman in Bruins history to score an overtime goal, which also proved to be his first NHL game-winning goal. Krug was frequently mentioned during the 2013–14 season as a strong contender for the Calder Memorial Trophy, awarded to the NHL's rookie of the year. He was named to the NHL's All Rookie Team and was the top scoring rookie defenseman in the league and was 4th in the league in the goals amongst rookies. His 14 goals and 26 assists helped the Bruins win the Presidents' Trophy, with the league's best record. In the 2014 Stanley Cup playoffs
In the 2014–15 Boston Bruins season, Krug tallied 12 goals and 27 assists and recorded a +28 plus-minus, the best of his career. The following season, he produced 44 points off of 4 goals and a career-high 40 assists.
On June 30, 2016, he re-signed a four-year deal worth an AAV of $5.75M with the Bruins.
Krug was born on April 12, 1991, in Livonia, Michigan, the son of Cheryl and Kyle Krug. Torey's brother, Adam, played college hockey at Adrian College and brother Matt played at Robert Morris University. Another brother, Zak, plays college volleyball at Siena Heights University in Adrian, Michigan. Torey admires the play of Pavel Datsyuk because "he's the most well-rounded player on the ice," and models his game after teammate Zdeno Chára. He calls his father his largest hockey influence.
Krug graduated with a degree in Political Science in May, 2017 from Michigan State. He originally enrolled within the school's Finance program, but switched majors to Pre-Law after claiming he didn't enjoy the content. Krug was forced to switch programs again after signing with Boston due to the mandatory courses in Law not being available online, leading him towards Political Science. He completed his remaining 38 credits online during the NHL off-season over the course of the next five years.