The former Hull City and Rotherham United player, 30, the club's fifth summer signing, arrives after a five-year spell at Southend United, where he made over 150 appearances for the Shrimpers.
On the Sheffield-born custodian, Weaver said: “Mark has a really big presence about him and with the experience he has got in the game, he’ll be able to communicate well and help others too.
“He’s very positive with his approach and really likeable, he collects crosses, kicks it a mile and is just the perfect fit for us.”
Oxley's career has also seen him play for Walsall, Grimsby Town, Burton Albion and Oldham Athletic and he admits that he is delighted to return to home soil in Yorkshire.
Oxley, whose arrival follows on from the signing of another experienced Yorkshireman in Rory McArdle, commented: “I’m delighted, the move was a no brainer for me having seen how well the club did last year and the progression they have made over the last few years, it’s something I wanted to be a part of.
“I’ve played quite a few games now in League One and Two and have a bit of experience at this level. I know what is required and I want to bring that in to help the lads as much as I can.
“To be back in Yorkshire with the solid group of lads that are here is nice to be a part of, it already feels like a big family, so I’m looking forward to what is to come.”