Koskinen, who could have become an unrestricted free agent July 1, is in his first season with Edmonton after signing a one-year contract May 1, 2018. The 30-year-old goaltender is 14-10-1 with a 2.78 goals-against average, a .911 save percentage and three shutouts in 27 games (24 starts) this season.
"I really believe we have a chance to win here," Koskinen said. "Being part of a winning team in the best league in the world, that's my dream and I'll try to help the team win as much as possible."
Koskinen has split time with Cam Talbot, who can become a UFA on July 1. Talbot, in his fourth season with Edmonton, is 9-13-2 with a 3.27 GAA and .894 save percentage in 27 games (25 starts) this season.
"[Talbot] is one of the best teammates that I've ever had...he's so supportive and I try to help him as much as possible when it's Cam's turn to play and I don't think [the contract] is going to change anything," Koskinen said. "We're playing on the same team and we both have the same goal: Edmonton Oilers need to win, so that drives us."
Selected by the New York Islanders in the second round (No. 31) in the 2009 NHL Draft, Koskinen spent the previous five seasons in the Kontinental Hockey League, including the past four with SKA St. Petersburg. In 2017-18, he ranked second in the KHL with a 1.57 GAA and a .937 save percentage.
He went 2-1-0 with a 4.33 GAA and .873 save percentage in four games with the Islanders in 2010-2011.
"I didn't have any personal goals when I arrived (in Edmonton)," Koskinen said. "I just wanted to do my job as well as possible every day and I'm not going to change that attitude, I just have to do my work every day as well as I can. ... If I do my work every day it's probably going to bring some good results and that's the only thing I can worry about.
"I've enjoyed my time here. The team is good. I think there is a huge potential here and I want to win. That's the biggest part (of) why I wanted to stay here and I truly believe this team and organization can prove many guys wrong."
In 31 NHL games (28 starts), Koskinen is 16-11-1 with a 2.97 GAA and .905 save percentage.
"When you see a guy who competes like that and never quits on anything... you know the top end is significant... I love what I see," Oilers coach Ken Hitchcock said.
The Oilers (23-23-3) are in sixth place in the Pacific Division and three points behind the Colorado Avalanche for the second wild card into the Stanley Cup Playoffs from the Western Conference.
"If you want to win something, you have to play your best at the end of the year, not at the start of the year," Koskinen said. "I have to improve and everyone else has to improve around me but the only thing I can take care of is myself."
NHL.com Correspondent Derek Van Diest contributed to this report