The 20-year-old hit 47 goals in 62 appearances during his time in Finland, having started his career at Independiente Medellin in his homeland.
He has scored 17 goals in 19 games this season for the Veikkausliiga leaders.
"I want to show the fans here what I did every day in Finland - to grow more as a player and as a person," he said.
Talking to RangersTV, Morelos added: "I did some research on the internet about the history and games - I know that it's a really big club and that they've played in really big tournaments.
"I want to do things the best way and try to do well in very match and every training session, to win trophies and to be a regular first team player.
"I know it won't be easy- it's going to be difficult because other team-mates will also be focused on this too.
"The most important thing is that I score goals - when the opportunity is there, I score."
Capped six times at Under-20 level, he is Ibrox manager Pedro Caixinha's sixth summer signing.
Morelos could make his debut against Progres Niederkorn after Rangers were drawn against the team from Luxembourg in the opening round of Europa League qualifying, with the matches played on 29 June and 6 July.
Cypriots AEL Limassol or St Joseph's of Gibraltar await the winners in the next round.
Rangers have signed Colombian striker Alfredo Morelos from HJK Helsinki on a three-year contract for an undisclosed fee.