The versatile 26-year-old, who spent last season on loan at German side Bayer Leverkusen, joins up with former national team boss Slaven Bilic at the Russian club on a three-year contract.
Lokomotiv spokesperson Kirill Kotov told the club's official website: "I am very pleased that we managed to strengthen the team with such a high quality player like Corluka.
"Vedran is one of the leaders of the Croatian national team. This is a versatile defender of the highest class."
Corluka joined Spurs from Manchester City for £8.5 million on deadline day of the 2008 summer transfer window and immediately became their first-choice right-back.
He was a key part of the side which reached the Champions League quarter-finals in 2011 but subsequent injuries and the emergence of Kyle Walker saw him shunted out of the first-team picture.
Corluka is the second Croatian to leave Spurs this summer following Niko Kranjcar’s move to Dinamo Kiev. The future of the third member of that contingent, star playmaker Luka Modric, is still uncertain following the departure of manager Harry Redknapp and Spurs denying the midfielder a move to Chelsea last summer.