The Nigerian midfielder has struggled to make any impact at the Portuguese giants and this becomes his third loan move since joining FC Porto's youth set up in 2012.
He joins Nigerian compatriot William Troost-Ekong at the Green Crocodiles.
"I'm delighted to join Bursaspor, I came here for business and I can't wait to show everyone what I can do," he told Bursaspor's official website.
"I spoke with some players who had previously played here in Porto and received positive feedback. I also found out during my own research that this is a great club," said Agu.
The 24-year-old spent the 2016/17 season on loan at Portuguese side Vitoria Setubal and made 34 appearances last season.
His performance in Portugal caught the eye of Nigeria coach Gernot Rohr who then handed him his Super Eagles debut in a 3-0 friendly win over Togo in June.
He has previously played on loan at Belgian side Club Brugge.