The 27-year-old had been linked with a move for a long time, but it has taken until the penultimate day of the transfer window for it to be wrapped up.
The Arsenal academy product has signed a four-year contract.
He follows Ilia Gruev, who joined from Werder Bremen earlier in the day.
It could means a relatively relaxed deadline day for Leeds with suggestions they may not chase a left-back after Luke Thomas joined Sheffield United.
But there are likely to be departures, and if a more established player like Luis Sinisterra or Illan Meslier were to move on, they may look into bringing someone else in.
Kamara's arrival, though, completes a good last week of business for Leeds, who have also signed Joel Piroe – who made a goalscoring debut at Ipswich Town – and right-back Djed Spence. They have also reintegrated Sinisterra and Willy Gnonto – who looks very likely to stay – into the side.
Kamara has been playing his football in Scotland since leaving Arsenal in 2017. He moved first to Dundee, where he broke into Finalnd's team, and moved on to Rangers two years later.
Kamara's ball-winning qualities, alongside those of Gruev, give Leeds a much more solid and flexible look.
Ethan Ampadu and Archie Gray have been the first-choice partnership in the first week of the season and have performed well. But there could be times when Ampadu is needed at centre-back and they have to be careful in not overloading Gray, a 17-year-old who has started every game this season.
The grandson of double European Cup finalist Frank can also play further forward behind the striker.
Kamara is Leeds' eighth signing of the window.