The forward has enjoyed two previous loan spells at the Liberty Stadium, the most recent coming during the second half of last season - during which he scored once in nine appearances.
Emnes has now signed on a permanent basis, putting pen to paper on a three-year contract after completing a medical.
"I'm delighted - I've waited a long time to become a Swansea City player," Emnes told the club's official website.
"From the minute I got here I had a good time. I've played some good games and I wanted to play for Swansea, while the club also wanted me.
"When I first arrived Swansea were in the Championship and I did well in the month I spent here.
"Last season I came back and with Swansea in the Premier League it was a good test for me to prove myself. I think I did well enough to earn my move permanently."
Emnes will now link up with his new team-mates as they fly out to America for a two-game pre-season tour, and he is excited about the new campaign.
"It's good to be a part of the squad right at the start of pre-season because you can prepare together as a team," said the Dutchman - who joins fellow new signings Lukasz Fabianski, Bafetimbi Gomis and Stephen Kingsley at the Liberty Stadium.
"There are some new players here so we can all get used to playing with each other and getting the best out of everyone too.
"In the last few games in the Premier League last season I really enjoyed testing myself against top players.
"As a forward you want to score goals and create some for the team too. Hopefully I will do that again here.
"This season I feel I will get more opportunities and that’s something I’m really looking forward to."