Rasmussen, 23, is a native of Arcadia and played collegiately at UCLA after starring at Polytechnic High School in Pasadena. In 2007, the Dodgers selected him in the 27th round of the amateur draft, but he decided to attend UCLA instead.
Rasmussen was selected by the Marlins in the second round of the 2010 amateur draft and then traded to the Houston organization on July 4, 2012 as part of the deal that sent Carlos Lee to Miami.
In three minor league seasons, Rasmussen is 20-21 with a 3.88 ERA in 60 games (53 starts), including 4-4 with a 4.80 ERA in 11 games (10 starts) at Double-A Corpus Christi in 2012.
Ely, 26, was acquired in a December 2009 trade with the White Sox and went 4-13 with a 5.70 ERA in 25 games (19 starts) over three seasons in Los Angeles.
The Dodgers now have 39 players on their 40-man roster.
Source: Los Angeles Dodgers