Nilsson launched his career in Sweden by playing three seasons with his hometown club, Lulea, two of them after being drafted in the third round (No. 62) of the 2009 NHL Draft.

The goaltender, who played for Sweden in the 2010 World Junior Championship, had a .918 save percentage and a 1.92 goals-against average in 31 games for Lulea during the 2010-11 season, his last in his home country.

In 2011-12 Nilsson joined Bridgeport of the American Hockey League and was named AHL Goaltender of the Month for February 2012, with a 6-0-1 record, a 1.26 GAA, a .955 save percentage and one shutout.

Nilsson played four games for the Islanders in 2011-12. He made his NHL debut Nov. 19, 2011, against the Boston Bruins, in relief of Rick DiPietro. Nilsson made his first NHL start two days later on the road against the Pittsburgh Penguins.

Nilsson made history on March 4, 2012, in a 1-0 victory against the New Jersey Devils, as he became the first Islanders goalie to get his first NHL win with a shutout. In 2013-14 he played 19 games for the Islanders and won five of his last seven decisions.

A restricted free agent, Nilsson signed with Ak Bars Kazan of the Kontinental Hockey League on May 26, 2014. The following season he had a 1.71 GAA and .936 save percentage to lead the club to the Gagarin Cup final.

On Oct. 4, 2014, the Islanders traded Nilsson, TJ Brennan and Ville Pokka to the Chicago Blackhawks for Nick Leddy and Kent Simpson, but Nilsson spent 2014-15 in the KHL and never played for Chicago. The Edmonton Oilers acquired Nilsson from the Blackhawks for Liam Coughlin on July 6, 2015, and signed him.

In 2015-16 Nilsson played 26 games for the Oilers and had 10 wins before being traded to the St. Louis Blues on Feb. 27, 2016, for Nicklas Lundstrom and a 2016 fifth-round draft pick. Nilsson played three games for the Blues. On July 2, 2016, he was traded to the Buffalo Sabres for a 2017 fifth-round draft pick.