The pair have combined to play in 853 NHL games.
Legace, 38, played last season in the German League after starting 26 games for the Carolina Hurricanes during the 2009-10 campaign. The Toronto, Ontario native spent six of his 11 NHL seasons with the Reds Wings, and in 365 career games compiled a 187-125-18 record with a .912 save percentage and a 2.41 goals against average.
Begin, 33, appeared in two games last season with the Nashville Predators, his fourth team in three years. The former second round pick in the 1996 draft has totaled 52 goals, 48 assists and 539 penalty minutes in 488 career contests.