Madrigal agreed to a minor-league contract with the Rays on Sunday, Marc Topkin of the Tampa Bay Times reports.
The 29-year-old will report to Triple-A Durham and will bolster the Rays' organizational depth at second base and third base. Before being dropped from the Angels' 40-man roster and electing free agency Thursday, Madrigal appeared in 15 games at the big-league level this season, slashing .273/.385/.295 with zero home runs, one stolen base, two RBI and seven runs across 52 plate appearances.