Foster's deal is worth a maximum of $43.5 million with $20.75 guaranteed, NFL Network insider Jason La Canfora reported, citing a team source. The deal includes a total of $18 million in base salary and bonuses in 2012 and is worth $30 million over the first three years.
Foster is now behind Adrian Peterson (seven years, $96 million) and Chris Johnson (six years, $55.26 million) as the third-highest-paid rusher in the league.
"Congrats to @ArianFoster for agreeing to a 5 year contract with the @HoustonTexans! Arian has showed tremendous class the last couple years," his agent, Mike McCartney, wrote.
Monday is the final day for teams to apply the franchise tag to players. Foster, who was set to become a restricted free agent, would have been a candidate for the tag.
Despite being limited to 13 games due to a preseason hamstring injury, Foster finished with 1,224 yards rushing, 617 yards receiving and 12 total touchdowns last season. The 2010 NFL rushing champion, Foster has been a Pro Bowl selection in each of the past two seasons.