Bougherra is an established Algerian international
Rangers have beaten off competition from West Brom to sign defender Madjid Bougherra from Charlton for £2.5m.
The 25-year-old was wanted by Hawthorns boss Tony Mowbray and a fee had been agreed between the clubs.
However, the Algerian centre half, who was also a target for Real Betis, has agreed a four-year deal at Ibrox.
"I came to football late but I want to progress and keep getting better - it is my dream to do good things for Rangers," he told the club website.
French-born Bougherra, who can also operate in midfield, joined Charlton from Sheffield Wednesday for £2.5m 18 months ago.
Earlier this month, Rangers manger Walter Smith saw a move for Watford's Danny Shittu break down over wage demands and he had been strongly tipped to make a bid for Cardiff central defender Glenn Loovens.
However, the capture of Bougherra, who will join international team-mate Brahim Hemdani in Glasgow, makes an approach for another defender unlikely.
"I spoke to Brahim about coming here and he spoke very well about the club, the facilities and the fans," added Bougherra.
"He pushed me to come here so I am very pleased to have signed for Rangers. They are a big club and I want to get into the team quickly.
"I know there are good defenders here so it will be hard. Hopefully I can move forward and learn from them.
"The team has done well in the Champions League and I have seen the atmosphere in the stadium during the derbies with Celtic.
"It looks fantastic and of course I would love to be involved in those matches this season."
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