The 25-year-old centre-back has featured just three times for Posh this season and had a loan spell at Northampton earlier in the campaign.
"Shaun was really eager about coming which delighted me," O's player-manager Kevin Nolan told BBC Radio London.
"His quality will create competition for our two centre-halves to make sure they are on top of their game."
Orient have won both their games since Nolan took charge last week, and moved into the League Two play-off places after beating Newport on Tuesday.
The 33-year-old hopes he can strengthen his squad further before the transfer window closes on Monday, having also brought in striker Armand Gnanduillet last Friday.
"I'll be speaking with the president [Francesco Becchetti] and his support staff about maybe getting a couple more in before the end of the window," Nolan said.
"Hopefully it is a positive relationship which gets us back to where we want to be, which is in League One."
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Leyton Orient have signed Peterborough defender Shaun Brisley on loan until the end of the season.