Wood, 25, has been with Trinity for the last two seasons after joining from Salford Red Devils.
However, he missed much of this campaign with a hamstring issue and he follows fellow hooker Kyle Wood out of Belle Vue.
Wakefield have signed Leigh Centurions No9 Liam Hood for 2022 to add to impressive youngster Brad Walker and Wood will now take up a deal with League 1 champions Barrow.
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“It’s a complete different change for me going part-time but it’s something I feel is needed after a big injury last year and I’m excited for it,” he said.
“My partner and I are having our first child in December as well, so being able to spend more time with them both will be great.
“Me and my agent spoke to a few big Championship clubs, but when I spoke to (players director) Andy (Gaffney) we got on really well and his ambitions for the club next year are something that excited me.
“I’ve also spoken to a few of the lads that are there and they have nothing but good things to say about the club so I feel it’s a good move for me.
“I’m looking forward to putting last year behind me and getting ripped into 2022 with the lads.”
Barrow head coach Paul Crarey said: “Josh is an all-action nine with Super League experience.
“He is a fearless defender and distributor and can also play in the halves.
“Josh comes with big wraps from former team-mates and coaches regarding attitude and application and we are delighted to have secured his signature.”