The Yankees made the announcement about Santos on Sunday, two days after the oft-injured reliever was placed on the disabled list because of elbow inflammation.
Lindgren, who was taken in the second round in the 2014 draft and who made his big league debut May 25, was optioned to triple-A Scranton/Wilkes-Barre on June 13. The Yankees tweeted that the rehab and recovery period should be no more than 12 weeks.
The Yankees signed Santos to a minor league deal on June 9 after he was released by the Dodgers. He eventually made two appearances for New York before injuring his elbow. The 31-year-old Santos made his debut in 2010 and had 30 saves for the White Sox a year later. But he spent much of the next three seasons with Toronto on the DL. He had season-ending shoulder surgery in 2012, then missed most of 2013 after elbow surgery. Last year he had a strained forearm.