The club inked Nieve to a Minor League contract and extended to the right-hander a non-roster invitation to Spring Training.
"He has a very good fastball. He gets it up to 96 mph," said Indians general manager Chris Antonetti. "He has good stuff. He has had some experience at the Minor League level and at the Major League level. He'll come into camp to compete for a spot, probably in the bullpen."
Nieve, 30, compiled a 7-9 record and 5.96 ERA in 25 outings (24 starts) for the Dodgers' Triple-A affiliate in Albuquerque last season. The Venezuela native has logged an 8-11 mark and 4.61 ERA in 99 career big league appearances. He pitched for the Astros in 2006 and '08 and the Mets in 2009-10.
Houston signed Nieve as an amateur free agent in 1999. The Mets claimed him off waivers in 2009. He briefly latched on with the Pirates and, for a second time, the Astros, before landing in Los Angeles.
In 198 Minor League appearances over 12 seasons, Nieve has racked up a 58-47 record and 4.12 ERA, with 840 strikeouts in 909 innings.
Cleveland claimed McDade, 23, off outright waivers from the Blue Jays, who drafted him in the sixth round of the 2007 First-Year Player Draft. To clear a spot for him on the 40-man roster, the Indians designated southpaw Chris Seddon for assignment.
"A switch-hitting first baseman, he's got a good approach at the plate and a very short, compact swing with some power," Antonetti said. "He's an interesting guy that our scouts have liked for a while."
McDade experienced his first taste of Triple-A last season and batted .338 (24-for-71) in 18 contests for Las Vegas. In 100 games at Double-A New Hampshire in 2012, the switch-hitter batted .275 with 15 homers and 49 RBIs. He is a career .265 hitter with 76 long balls over six Minor League seasons.