The ex-Republic of Ireland striker departed his position as manager of Israeli club Maccabi Tel Aviv last week.
Keane may not have felt the region was safe for himself and his family, considering the Israel-Hamas conflict.
"It has been a tough decision for me to leave Maccabi Tel Aviv FC," he told Betway.
"I would like to thank all the players, coaches, owners and especially the fans for making this an unforgettable season.
"I am very proud of the everything we have achieved together as a team, and most proud of the hard work and dedication that resulted in us winning the Toto Cup and league title, guaranteeing Maccabi a Champions League spot.
"I think the hardest thing for any coach is going in at a new club and winning the league, because it’s done over a long period of time. I’m very blessed and honored to have done that.
"We all got together to celebrate with the players and my staff. I thought it was important to all celebrate together, because the guys in the background have worked tirelessly for the whole season.
"We had a nice, low-key dinner and some music, and it was a great evening. For a first season, it couldn’t have gone any better. I wish we’d have won the other cup, but maybe I’m getting a little bit too picky!
"If you asked me before the season whether we could achieve what we have, I’d have said it would be tough, but I loved the challenge and I’m very glad we did it. To finish my first season with two trophies is very special. Wishing everyone involved at the club all the best for the season ahead."