Davidson, a 26-year-old defenseman, has five points (three goals, two assists) in 36 games this season. He can become a restricted free agent July 1.
The Islanders, who visit the New Jersey Devils on Saturday (6:15 p.m.ET; MSG+, MSG+2, NHL.TV) are tied with the Columbus Blue Jackets for the second wild card into the Stanley Cup Playoffs from the Eastern Conference.
"It's a great oppotunity for me, going into a playoff run with those guys," Davidson said. "It's tough to say goodbye, but on a good note, I think the playoff run is going to be awesome for me."
Selected by Edmonton in the sixth round (No. 162) of the 2010 NHL Draft, Davidson has 20 points (eight goals, 12 assists) in 137 NHL games.
Davidson was traded by the Montreal Canadiens to the Oilers for David Desharnais on Feb. 28, 2017, one day before the NHL Trade Deadline last season. This season's trade deadline is Monday at 3 p.m. ET.
"It's a little easier transition the second time around. I know how to deal with it, I know how to handle myself and I'm excited to put my best foot forward," Davidson said. "I started to play some of my best hockey over the last month and maybe that is something [the Islanders have] seen," he said.
The Oilers, who visit the Los Angeles Kings on Sunday (10 p.m. ET; SN, SN360; CITY, FS-W, NHL.TV) are 18 points behind the St. Louis Blues for the second wild card in the Western Conference.