Hailing from Nøtterøy outside Tønsberg, Johansen made his debut for Teie IF in the 4. Divisjon at the age of 14. After training with the Tippeligaen sides Sandefjord and Odd Grenland, he was invited on a trial with Manchester City. After Johansen got a fracture in the foot before his trial, his family managed to get a trial with his brother Tobias instead, who also plays as a goalkeeper. Tobias impressed in the trial and got a contract with Manchester City. Eirik later got a new trial with City, and when he joined the Manchester City Academy in August 2008, their mother and two younger brothers also moved to England. Tobias returned to Norway and Kongsvinger in 2010.
Club career
Manchester City
Johansen was training regularly with City's first team in the 2010–11 season, and signed a new two-year contract with the club in May 2011. He made his debut for the first team when he played seven minutes of the friendly match against League of Ireland XI on 30 July 2011. After playing regularly for the reserves during the 2011–12 season, Johansen signed a professional contract with the club in July 2012. Johansen played a number of pre-season friendlies ahead of the 2012–13 season, and started the season on the bench during Manchester City's 2012 FA Community Shield win. He spent most of the season playing in the reserve team, before joining League One side Scunthorpe United on loan in March 2013 for the rest of the season as cover for the injured number one 'keeper Sam Slocombe who was out for six weeks with a torn thigh muscle. His debut for Scunthorpe United came in a 1–2 home defeat against Coventry City Johansen played the full 90 minutes. In January 2014, Johansen joined Norwegian club Sandefjord on a six-month loan-deal where he was reunited with his old goalkeeping-coach from Teie, Hans Petter Olsen. When signing Johansen, the club stated that they wanted him as their new first-choice goalkeeper, as the first-choice in the previous season, Iven Austbø, had transferred to Viking. Johansen was also linked with a move to Scottish Premiership sideRoss County, but the move fell through.
Johansen made his second appearance for NYCFC, in a 1–0 loss in the US Open Cup against the New York Cosmos, on 15 June. On 23 October, he made his first league appearance, starting in a 4–1 win over Columbus Crew, in the season finale. Johansen then started NYCFC's first ever playoff game on 30 October, a 0–2 loss to Toronto FC.
Sandefjord
In December 2017, Johansen re-joined Sandefjord on a permanent contract, signing for two years at the club.
On 9 January 2019, Johansen signed with SK Brann on a four-year contract. On 15 June 2020, Johansen signed a loan deal with Kristiansund.
International career
Johansen has represented Norway at various youth levels, and was in May 2012 training with the senior team in the absence of regular goalkeepers Espen Bugge Pettersen and Rune Jarstein.