The pair both signed three-year contracts with the Glasgow giants on Wednesday and will be made immediately available for Thursday’s Europa League play-off meeting with Maribor in Slovenia.
US skipper Bocanegra has joined ‘Gers after spending one season with French club Saint-Etienne whom he joined from Stade Rennes in summer 2010.
The 32-year old defender, who arrived in Rennes in June 2008 following a four-and-a-half-year spell with English Premier League club Fulham, was originally not for sale by Saint-Etienne but Rangers managed to negotiate a deal with Ally McCoist determined to strengthen his defence.
24-year old midfielder Bedoya arrives at Ibrox from Swedish club Orebro after signing a pr-contract agreement in January which was initially set to see him join in December but that has been brought forward to this transfer window.
The pair will join fellow USA international Maurice Edu at the club which has won the past three Scottish titles.