The fee could ultimately rise to £2.5million for the Republic of Ireland defender, 21, who joined the Baggies from Manchester United last summer and made 42 appearances, scoring three times.
Three quarters of that extra £1million is based on appearances plus a further £250,000 if the Black Cats retain their top-flight status this season or regain it during McShane's stay in the north-east.
West Brom manager Tony Mowbray said: "I want to thank Paul for his contribution last season. He's a terrific lad with a terrific attitude to football.
"But Paul intimated to me in very strong terms that his ambitions lay away from this football club.
"I've said it many times before that I want players here who want to play for the shirt so that we can move the club forward together.
"We've now sold three players who made it clear they wanted to leave.
"We now have an opportunity to build a new team with players who are fully committed to taking the club forward."
McShane is Sunderland boss Roy Keane's sixth signing of the summer after recruiting Greg Halford, Russell Anderson, Michael Chopra, Kieran Richardson and Dickson Etuhu, but he has missed out on several high-profile signings.
Keane discussed his pursuit of McShane earlier on Thursday, when he said: "We are in talks with West Brom at the moment and we hope that will be concluded over the next few days - we hope.
"Paul is a player I know and I like. He's a good character. We need competition for places and Paul would bring that.
"I don't like talking about players who are under contract at other clubs, but we are hopeful a deal can be done. But we will have to wait and see."