The Londoners, who failed in a double swoop for the pair at the end of the January transfer window, announced: "We have agreed a £2m deal with Leeds United for goalkeeper Paul Robinson, subject to agreeing personal terms with the player and a medical. We hope to conclude the deal early next week."
The Hull born international will not be involved in this weekend's Premiership farewell at Chelsea ahead of the summer move to White Hart Lane.
PFA deputy chief executive Mick McGuire also revealed that they had made a "fantastic bid" for Milner too.
McGuire, who acts as Milner's agent in his role with the Professional Footballers' Association, said: "It is true to say Tottenham Hotspur made a fantastic bid for James and I have discussed the matter with both the Leeds chief executive, David Richmond, and I have also spoken at length with Tottenham chairman Daniel Levy.
"In fairness, the bid was tremendous and the way both clubs have conducted themselves in this matter has been thoroughly professional and at no point did we feel that Leeds were trying to push James out the door.
"James is totally committed to Leeds and wants to stay at Elland Road and he feels that another year with added responsibility can only enhance his ability as a player," he added.
The Hull born international will not be involved in this weekend's Premiership farewell at Chelsea ahead of the summer move to White Hart Lane.
PFA deputy chief executive Mick McGuire also revealed that they had made a "fantastic bid" for Milner too.
McGuire, who acts as Milner's agent in his role with the Professional Footballers' Association, said: "It is true to say Tottenham Hotspur made a fantastic bid for James and I have discussed the matter with both the Leeds chief executive, David Richmond, and I have also spoken at length with Tottenham chairman Daniel Levy.
"In fairness, the bid was tremendous and the way both clubs have conducted themselves in this matter has been thoroughly professional and at no point did we feel that Leeds were trying to push James out the door.
"James is totally committed to Leeds and wants to stay at Elland Road and he feels that another year with added responsibility can only enhance his ability as a player," he added.