Loffreda will arrive at Welford Road after this year's World Cup in October.
The 47-year-old will succeed Pat Howard, who is returning to Australia in the summer.
Loffreda has been linked with the Tigers post for several months, and was an overwhelming favourite for arguably English club rugby's top job.
And he could inherit a Leicester side at the peak of its powers.
Tigers have already won the EDF Energy Cup this season, while they meet Wasps in next month's Heineken Cup final and are also contesting the Guinness Premiership title.
Loffreda won 44 caps for Argentina, and took over as Pumas coach in 2000.
Announcing the appointment, Tigers chairman Peter Tom said: "Marcelo has done a marvellous job in taking Argentina to the top ranks of the international game.
"He is recognised as a top-class coach, and has developed a squad of quality players to the point where they have reached number six in the world rankings.
"I have been impressed by his thoughts on the game, his approach to coaching and his ideas on how to take Leicester Tigers forward.
"We look forward to the fresh input from Marcelo, as well as the continued development of the existing staff and players at the club."
With Howard due to depart at the end of this season, forwards coach Richard Cockerill will take charge of team affairs, assisted by the rest of the Tigers coaching team, until Loffreda's arrival.
Loffreda was a guest of the club at Saturday's Heineken Cup semi-final victory over Llanelli Scarlets, having first been linked with Tigers last autumn.
He was at the helm when Argentina recorded their first victory over England at Twickenham - a 25-18 success five months ago that heavily contributed towards head coach Andy Robinson losing his job - while the Pumas will arrive in France for this year's World Cup as a powerful force.
They are in the same pool as France and Ireland, but possess the capability to upset both teams, and a quarter-final place is not beyond them.
Loffreda said: "The name of Leicester Tigers is renowned throughout the rugby world.
"To be invited to join this great club as head coach was an honour not only for me, but also for the people who love rugby in Argentina.
"Leicester is a club with a wonderful history and has supporters who are passionate about their club. I know there is also a squad of players with a hunger and drive to be the best.
"There are some exiting times ahead for us all at Tigers."
Loffreda will inherit a Leicester squad that includes Argentine internationals Marcos Ayerza and Alex Moreno, while New Zealand centre Aaron Mauger has already been confirmed as a post-World Cup arrival in the midlands.