NFL Media's Mike Garafolo reported that the deal is worth $1.5 million with an additional $2 million in incentives.
Foster worked out for the 'Fins on Monday. The 29-year-old runner had a second visit planned later in the week with the Lions, but Detroit didn't get a chance to lure him away.
"I know that this league knows that when I'm on the field, I'm one of the most productive doing it," Foster said after inking his new deal.
Cut by the Texans in March, Foster is rebounding from the ruptured Achilles tendon he suffered in October. Expected to be ready for camp, the undrafted workhorse has been running for months and spent much of his offseason working out at IX Innovations, the Houston-based training facility owned by his brother, Abdul Foster, who said in March: "Arian's doing great."
Miami always made sense as a landing spot for Foster, who has a chance at major snaps alongside second-year back Jay Ajayi. Playing under creative coach Adam Gase is a plus, while Foster -- assuming he regains his old form -- bolsters a position that desperately needed help.
Foster's 2015 season was a total wash, but he was outstanding for sections of the previous campaign, running for 1,246 yards and eight touchdowns. There were moments in 2014 where Foster looked as good as ever.