The Colombian joined the Cherries on loan in the late stages of the window, with Jaidon Anthony heading in the opposite direction as part of the deal.
There had been speculation regarding his future throughout the summer, with Brentford among the clubs linked with the 24-year-old.
However, it was Bournemouth who secured his services with a dramatic late deal.
His agent, Simone Rondanini, has issued a social media message following the move.
Posting on Instagram, he said: “Happiness has to be sought and, sometimes, you have to fight to get it. Together we made it easier. ‘Just say no to deal breaker’, YOU WIN!”
The post has since been edited, with the caption now reading: “It hasn't been easy but we're taking the good out of this experience. Now it's time to bring your magic to this new elastic. Last minute deal!”
Sinisterra departed West Yorkshire with 26 Leeds appearances on his CV, with his future beyond the end of his loan stint on the coast uncertain.