The 22-year-old is believed to have held talks with the Baggies earlier this week, despite reported interest from Arsenal.
And Doumbia, who is thought to cost around £2 million, has revealed that the increased chances of regular first-team action led him to opt for West Brom.
"I have no regrets about leaving Rennes, I go quietly and with a smile on my face, I have no grudges against the club," he told 20Minutes in France.
"I felt a lot of desire from them, obviously it is less glamorous than Arsenal, but I will be able to continue my progress.”
Tongo, who has been at Rennes since 2009, learned his trade at Ligue 2 outfit LB Chateauroux, before making the transition to the top flight, and he is now eager to test his talents in the Premier League.
"The Premier League thrills me and I hope this is the beginning of a new adventure."