In a corresponding roster move, the Marlins designated center fielder Kevin Mattison for assignment.
Toronto designated Dyson for assignment last week to make room on their roster for utility player Mark DeRosa.
Dyson made his major league debut in 2012, appearing in two games for the Blue Jays. The 24-year-old allowed three runs on four hits with two walks and one strikeout over two-thirds of an inning, good for an ERA of 40.50.
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The right-hander fared a bit better in the minors last season, as he posted a 3.04 ERA over 39 appearances, including six starts, for the Blue Jays' high- and Double-A clubs.
Mattison also made his major league debut this season. He didn't collect a hit in five at-bats over three games with the Marlins. The 27-year-old hit .241/.310/.394 with 23 doubles, six triples, 13 home runs and 26 stolen bases in 38 attempts for Miami's Triple-A affiliate.