Watson will be replacing Usman Khawaja, who played in the first two ODIs, before heading to India along with the last group of Test players as Cricket Australia decided to send the squad to the subcontinent in three separate groups.
Australia has already won the first two matches and would look to seal the five-match ODI series against the West Indies in the third one-dayer in Canberra, where Watson will play as an opening batsman.
"Shane Watson comes back into the squad against West Indies as an opening batsman. Shane has recovered from his injury and we look forward to seeing him get back to his best," the national selector John Inverarity said.
After recovering from a calf injury, allrounder Watson returned to action as a non-bowling batsman and played a Sydney club game and an interstate one-dayer.
Australia will play two warm-up games, scheduled to be held from February 16-18 and February 12-13, before the first Test in Chennai is scheduled for February 22-26.
Australia's 13-man squad for 3rd and 4th ODI: Michael Clarke (c), George Bailey, Ben Cutting, Xavier Doherty, James Faulkner, Aaron Finch, Phillip Hughes, Mitchell Johnson, Glenn Maxwell, Clint McKay, Mitchell Starc, Matthew Wade, Shane Watson.
