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"Coming back to the Islanders is exciting for me," Martin told Newsday. "In my heart, I was hoping for this."
The 29-year-old forward had 12 points (three goals, nine assists) in 50 games with the Maple Leafs last season and did not play in the Stanley Cup Playoffs, when they lost to the Boston Bruins in seven games in the Eastern Conference First Round.
"I do think I can contribute in a similar way that I contributed before," Martin told the newspaper. "I'm as hungry as I've ever been. Last year wasn't a lot of fun for me in a lot of ways. To get another opportunity with this team is unbelievable for me."
Martin was selected by the Islanders in the fifth round (No. 148) of the 2008 NHL Draft and played seven seasons with them. He led the NHL in hits for five straight seasons from 2011-16 and his 382 hits in 2014-15 are the most in a season in NHL history. Martin signed a four-year contract with the Maple Leafs as an unrestricted free agent July 1, 2016.
In 570 NHL games with the Islanders and Maple Leafs, Martin has 109 points (50 goals, 59 assists). His 2,475 hits are the most since he entered the NHL in 2009-10.
"I wouldn't say I'm surprised that I was being moved," Martin said. "It's no secret how the second half of the season played out for me last year. I had a pretty good idea when I was not moved at the deadline I'd get moved in the summer."
McAdam, 23, was selected by the Islanders in the third round (No. 70) of the 2013 NHL Draft. He went 13-10-6 with a 2.84 goals-against average and .910 save percentage in 29 games with Worcester of the ECHL last season, and 5-2-0 with a 2.77 GAA and .903 save percentage in nine games with Bridgeport of the American Hockey League.