The 21-year-old put pen-to-paper on the deal after both clubs agreed a fee of £75,000 for his signature.
Pompey and a number of other clubs had been interested in Forde after he impressed for Barry Town this season.
Hammers boss Glenn Roeder has moved to sign the former Galway United ace to act as cover for first-choice goalkeeper David James and with Shaka Hislop set to leave in the summer Roeder wants a replacement ready.
The Republic of Ireland Under-21 international has no fears about making the step up from the League of Wales and he insists he will fight for a place in The Hammers side.
"There is no point coming just to play in the reserves," Forde told the club's official website.
"I'm looking to make the first team, though obviously I am a great admirer of David James, who I regard as the number one for England in the World Cup.
"I have always looked up to him, and hopefully I can learn from him.
"Kenny Brown is the manager at Barry Town and put me in touch, and I trained with West Ham for two weeks at the start of the year.
"I have thoroughly enjoyed it and Ludo Miklosko has been great to work with.
"Glenn Roeder told me that he brought Kevin Phillips from Baldock Town to Watford, so the gap is not impossible.
"And, at 21, I'm only a baby as far as keepers are concerned.
"I have played every game since joining Barry Town from Galway in Ireland this summer, and I opted for West Ham above Portsmouth and other clubs that wanted me."
