The American goalkeeper says he will retire at the end of this season.
"Brad's had a fantastic career and this is a special moment for him," Pochettino told the Spurs website.
"He is a top man, a fantastic professional and one of the best goalkeepers in England.
"It's been a pleasure to work with him, to get to know him and spend time with him this season. I can only congratulate him on his career."