The 29-year-old, who was captain at Spartak, can also play in central defence and brings a wealth of experience from his country's World Cup 2006 and Euro 2008 campaigns.
Hammers boss Gianfranco Zola is delighted to have signed a player who is used to Champions League and UEFA Cup level.
"I am pleased to have Radoslav here," Zola told the club's official website.
"He has a lot of experience with the national team and he will give us competition in a midfield - which is already very strong. I am sure he will help us with what we are trying to achieve this season."
Kovac, who had his medical earlier today, watched his new team-mates in training before the deal was completed tonight.
West Ham chief executive Scott Duxbury confirmed his club have an option to make the signing permanent if it is agreeable to both parties.
"I am delighted we have managed to secure the services of a proven international like Radoslav, ahead of interest from clubs at home and abroad," he said.
"He brings considerable quality and will fit right into Gianfranco Zola's talented squad. The deal is such that the manager will be able to sign him permanently in the summer if he so wishes."