Cleveland designated Cimber for assignment last week. He appeared in 14 games for the team in 2020, posting a 3.97 ERA and 1.32 WHIP with five strikeouts.
The 30-year-old is projected by MLB Trade Rumors to earn between $800,000 and $1 million in arbitration.
Urena had been the Marlins' longest-tenured player. The 29-year-old reportedly would have been non-tendered ahead of Wednesday's deadline, according to Craig Mish of the "Swings and Mishes" podcast.
The Marlins' Opening Day starter in 2018 and '19, Urena started just five games for the team last season, crafting a 5.40 ERA and 1.50 WHIP while striking out 15 and issuing 13 walks.