On a busy day for Blues, the winger joined Alex McLeish's side for an undisclosed fee from Club America in Mexico.
Beausejour joined defender Martin Jiranek and midfielder Alexander Hleb in arriving at the club on deadline day.
The 26-year-old is an exciting left-sided attacker who plays primarily on the left but also up front and had an impressive World Cup campaign.
McLeish told bcfc.com: "Beausejour is an excellent, left-sided midfielder who had a tremendous World Cup with Chile - he was their star player against Spain - and also played very well in a pre-season friendly against Manchester City recently.
"He has been on our list of targets for a long time because he is strong and quick with the ability to beat his man and get crosses in."