Carroll's agreement with the Twins is for two years and close to $7 million pending a physical, according to the source.
Carroll, 37, hit .290 in 146 games with the Los Angeles Dodgers last season. He posted a combined .385 on-base percentage out of the leadoff and No. 2 spots in the batting order.
The Twins went with Tsuyoshi Nishioka, Trevor Plouffe and Alexi Casilla as their principal shortstops in 2010. Minnesota's shortstops hit a combined .238 with a .612 OPS -- 26th among the 30 major league clubs.
Atlanta, Philadelphia, Detroit, Toronto, Colorado, Cleveland and the Dodgers were among the other clubs that had reportedly expressed interest in Carroll this offseason.
Jerry Crasnick is a senior MLB writer for ESPN.com.