The Liverpool-based side also took former midfielder Steven Pienaar back on loan from Spurs for the rest of the season, David Moyes' side said on their website after the window had officially shut.
The South African has suffered a series of injury problems at Tottenham since joining from Everton in January last year.
Tottenham's capture of injury-prone Frenchman Saha was the biggest surprise on a traditionally busy date for Spurs, who are allowing little-used frontman Roman Pavlyuchenko to talk to Lokomotiv Moscow in his native Russia after agreeing a fee.
Spurs boss Harry Redknapp told reporters the deal for former Manchester United forward Saha was a loan until the end of the season with an option to buy.
The Premier League challengers have also let defender Sebastien Bassong join Wolverhampton Wanderers on a six-month loan. Reports said Spurs were trying to bring in New Zealand centre-back Ryan Nelsen from Blackburn Rovers as the window closed.
Jelavic has joined mid-table Everton on a four-and-a-half year contract for an undisclosed fee with media reports estimating the transfer fee to be around eight million pounds.
Jelavic, 26, started his first-team career at Hajduk Split before having spells at Zulte Waregem in Belgium and Rapid Vienna before joining Rangers in 2010.
He scored 36 goals in 55 matches for the Ibrox side and is a key addition for Everton, who have been short of forwards.
Jelavic and Pienaar became Everton's third and fourth signings in the January transfer window after the arrivals of Ireland midfielder Darron Gibson from Manchester United and American Landon Donovan on loan from LA Galaxy.
