Page, 20, has agreed a two-and-a-half-year contract at The Valley.
He made three first-team appearances for West Ham, all in the Europa League, and has previously been on loan at Coventry City and Cambridge United.
"He's quick, likes to get forward and is a good crosser. I really like that in a full-back," Charlton manager Karl Robinson told the club website.
"I got a chance to see him during his loan spell at Coventry and he's a left-back that fits in well with our system.
"We're building a squad here to get into that top six and Lewis will be an important part of what we are trying to do."
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League One club Charlton have signed left-back Lewis Page from West Ham for an undisclosed fee.