The 21-year-old arrives from the Premier League side on a permanent deal to boost Danny Cowley’s options.
The Portsmouth-born Northern Ireland under-21 international will provide cover for Manchester City loanee Gavin Bazunu, after Alex Bass joined Bradford City on loan.
The possibility of Northern Ireland involvement for Webber would increase the chances of Pompey having three players called up for their countries - and the flexibility to postpone fixtures over an international break.
The next of those arrival in March with Pompey due to go to Bolton on March 26.
Cowley told the club’s official website: ‘We’re delighted to bring Ollie into the group and he’s someone we were able to have a look at when he came in just before Christmas.
‘He’s had a great education at Crystal Palace and as well as being a good shot-stopper, is comfortable with the ball at his feet and has excellent distribution skills.
‘Alex Bass has gone out on loan to Bradford because we’ve taken a long-term view and it’s so important that he plays in the second half of this season.
‘Ollie has come in and is a young keeper who wants to improve every single day. We like to recruit players who have a burning ambition to get better.’
Webber’s signing follows the additions of loanees Hayden Carter and Tyler Walker, with Denver Hume's permanent £200,000 arrival from Sunderland close to completion.
Ellis Harrison, John Marquis, Paul Downing and loanees Gassan Ahadme and Miguel Azeez have all left this month.
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