It was reported on Friday that a £15m deal had been agreed between the two clubs, with Pulis admitting that he had spoken to Burnley counterpart Sean Dyche about the player.
Gibson was left out of the squad for Middlesbrough's 2-2 draw with Millwall at the Den in their Championship opener on Saturday and speaking after the game, the Boro boss confirmed that the 25-year-old would be leaving the club.
“He's going, it's agreed, it's done and we want to thank Ben, an absolutely fantastic professional.
“In the six months I've had at this football club he's as good a professional as I've ever worked with and I spoke to Sean Dyche and Dychey's got a real, top, top player.
“I think it'll go through over the weekend, I think it's all done, I think everybody has agreed it and it's just a case of him doing his medical and then that will be it.”