Olmos, 25, was 1-1 with a 3.55 ERA in 20 appearances with Tacoma, including two starts. His only previous experience in the majors is five relief appearances for Miami in 2013.
Rasmussen, 26, was 2-1 with a 16.20 ERA in eight relief appearances after being acquired in a trade with Toronto on July 31. He pitched in each of Seattle's three games at Boston over the weekend, working three innings and allowing five earned runs.
The Mariners announced the moves before Monday night's game at Texas.