Norén was born in Stockholm, where he started playing golf at the Haninge Golf Club. He attended Oklahoma State University in the United States before turning professional in 2005.
Norén gained a place on Europe's second tier Challenge Tour by reaching the final stage of the European Tour qualifying school at the end of 2005. In his rookie season he claimed his maiden professional victory at the Rolex Trophy, and ended the year in 3rd place on the Challenge Tour Rankings to graduate to the elite European Tour for 2007.
Norén had a solid rookie season on the European Tour in 2007 and improved on that the following year to finish in 31st place on the Order of Merit. He made the cut at the 2008 Open Championship and was in the top 10 going into day 3, before eventually finishing in a tie for 19th place.
Norén won his first title on the European Tour in September 2009 at the Omega European Masters, where he finished 20 under par to win by two strokes over Bradley Dredge. Norén finished the season ranked 25th on the Race To Dubai.
In June 2011, Norén won his second European Tour title at the Saab Wales Open played at The Celtic Manor Resort. He won by two strokes from Grégory Bourdy and Anders Hansen finishing at 9 under par. This victory secured him of a place in the WGC-Bridgestone Invitational at Firestone Country Club in August. The following month, Norén won his third European Tour title at the Nordea Masters in his home country of Sweden. He won from wire-to-wire, the first time in his career he had achieved this feat, and opened up an eleven-stroke margin after the third round. Despite difficult conditions in the wind on the final day, Norén finished seven strokes ahead of Richard Finch. He finished the season ranked 14th on the Race to Dubai.
After two positive seasons in 2012 and 2013, where he registered third places at the Aberdeen Asset Management Scottish Open and the Alfred Dunhill Links Championship, Norén missed most of 2014 with tendonitis in both wrists.
Norén came back to competitions in January 2015; in June he won his fourth European Tour title by capturing the Swedish Nordea Masters for the second time in his career. He won by four strokes from Søren Kjeldsen, having held a two-stroke lead after 54 holes.
In the second half of 2016 Norén would hit outstanding form, winning four in eleven starts on the European Tour. In July he won the Aberdeen Asset Management Scottish Open, the event before The Open Championship, for his fifth European Tour victory. He won by a single stroke from the Englishman Tyrrell Hatton. This win continued his trend of holding the 54-hole lead in every event that he had won on tour. It also represented the first time that Norén had won in back-to-back seasons.
After finishing runner-up at the Paul Lawrie Matchplay in August, he won the Omega European Masters in September, beating Scott Hend at the first playoff hole. A month later, he captured his third win of the season at the British Masters at The Grove. The win lifted him to the 18th place of the Official World Golf Ranking.
In November, Norén won his fourth title of 2016 at the Nedbank Golf Challenge, capturing $1,166,660, the largest in his career so far. He began the final day six shots behind Wang Jeung-hun only to finished six strokes ahead after a record round of 63 (−9). With the win, he moved to third in the Race to Dubai ranking, and to ninth in the Official World Golf Ranking, becoming only the fourth Swede to enter the top ten of the OWGR after Henrik Stenson, Robert Karlsson and Jesper Parnevik.
European Tour playoff record (1–0)
CUT = missed the half-way cutMost consecutive cuts made – 2 (three times, current)
Longest streak of top-10s – 1 (twice)
WD = withdrew
"T" = tied
Results not in chronological order prior to 2015.
DNP = Did not play
QF, R16, R32, R64 = Round in which player lost in match play
"T" = tied
AmateurEisenhower Trophy (representing Sweden): 2004
Palmer Cup (representing Europe): 2004 (winners), 2005
ProfessionalRoyal Trophy (representing Europe): 2010 (winners)
Seve Trophy (representing Continental Europe): 2011
World Cup (representing Sweden): 2011, 2016