The Norwegian beat team-mate Virgil van Dijk, Dundee forward Greg Stewart and Aberdeen striker Adam Rooney to the prize.
John Hughes won the manager of the year award after leading Inverness to the William Hill Scottish Cup final and a probable top-three place in the Scottish Premiership.
Johansen has scored 12 goals so far in his first full season at Celtic Park and become an increasingly influential figure
Hughes finished ahead of Hearts head coach Robbie Neilson, Aberdeen boss Derek McInnes and Celtic's Ronny Deila.
But there was more success for the newly-crowned champions as Celtic defender Jason Denayer claimed the young player prize.
Despite Hearts' runaway success in the Scottish Championship, Hibernian midfielder Scott Allan was named player of the year in the division.
Aberdeen striker Declan McManus won the League One award after hitting 23 goals during a season-long loan spell at champions Morton while Arbroath striker Bobby Linn was voted best player in League Two.
St Mirren midfielder Stephen Mallan won goal of the season for his solo effort against Dundee at Dens Park, when he shimmied his way from his own half to the edge of the box before curling home.
Dundee United forward Jordan Moore won a special merit award after overcoming skin cancer to bounce back with a season on loan at Queen's Park.
Source : PA
Source: PA