The 29-year-old midfielder was offloaded by former Black Cats boss Paolo Do Canio as part of a comprehensive summer rebuilding project at the Stadium of Light.
He was not allowed to go cheap, with West Brom making the Benin international their record signing.
A transfer away from Sunderland had been mooted for some time - with Sessegnon having proven himself on the Premier League stage - but he is adamant that he was happy on Wearside and only accepted a new challenge once an enticing opportunity was put to him.
He told the Sunderland Echo: "I didn't sense that I was going to leave Sunderland, but that's the life of a footballer.
"If a club wants you and they accept an offer, then that's what happens. That's football.
"I never asked to leave the club. But the club accepted the offer and then I had the choice to come to West Brom.
"It's football and I had the chance to continue playing in the Premier League. It's a good opportunity for me.
"I had three very good years at Sunderland with some great moments. I will always remember the good memories there and the people at the club."