The 27-year-old, who has been a regular for the Addicks lately due to an injury to Ben Hamer, has moved on a permanent basis until the end of the season.
It will be Alnwick's second spell at the O's after he made eight appearances on loan from Tottenham in 2011.
Orient boss Russell Slade made the move after Hull recalled loanee Eldin Jakupovic earlier this week, and Alnwick is set to make his debut at Rotherham on Saturday.
- Sports & Recreation
- Ben Hamer