Blackburn have signed defender Doneil Henry on a month's loan from West Ham.
Miles Addison has joined Blackpool on a month's loan from Bournemouth.
Carroll, 21, who is primarily a left-back but can also play in central midfield, had two separate trial periods with the Terriers and will now join up with the club permanently this summer for pre-season training.
"Jake impressed me a lot when he was here a few weeks ago," Town manager Mark Robins told the club's official website. "He is left-sided, quick, powerful and has a good attitude with an aptitude to learn quickly.
"He will have to adapt to the style of football in England, but he arrives with the challenge of breaking into our first team.
"Ireland is an interesting market for English clubs. A lot of talented Irish players arrive in England at 16 years old, in the same way that we recently recruited the country's Under-16 captain Danny Kane from Cherry Orchard, whereas others are identified after emerging in a League of Ireland team at aged 20 or 21, such as James McClean and Seamus Coleman. Jake comes under the latter of those two routes."
London-born Carroll grew up in Lucan, Ireland and played the majority of his youth football for Home Farm but had a short spell at Belvedere before joining St Patrick's Under-20 side in 2010.
During this time he was capped by the Republic of Ireland schools side whilst studying at university.
Since breaking into the first team he has made more than 50 appearances for the club, which includes Europa League appearances.