Talei, 27, who has won 16 caps for Fiji, also joins from Worcester Warriors - for whom he played more than 50 games.
"I'm really excited to be joining Edinburgh," Talei told www.edinburghrugby.org today. "I was at the club earlier this month and met up with Rob Moffat and I know that they play the same type of rugby that I want to play.
"I'm looking forward to being part of an open style which I think can suit my off-loading game," he explained.
Edinburgh's head coach Rob Moffat said: "We're pleased to have signed Netani. We've watched him closely and have done our homework on him.
"We believe he'll give us that dynamic ball-carrying ability in the back-row and we feel his strengths will dovetail nicely with how we play."
Grove, 22, will now compete alongside Nick De Luca, John Houston and Ben Cairns for an Edinburgh midfield berth and Moffat today welcomed his arrival.
"Quality brings out intense competition and that is good for the team and I'm delighted to welcome Alex to the club."
Grove, who won three caps for Scotland during last year's Autumn Tests, expressed his gratitude to Worcester Warriors for their support in his loan move.
He added: "The move is to give me the best chance to continue my international career and it's a great opportunity to play with the quality backs in the Edinburgh team.
"Edinburgh play a high-tempo game and I'd like to think that plays to my strengths."
Talei, who can play either at No 8 or at blindside flanker, is renowned for his high work-rate and helped Fiji reach the knockout stages of the last Rugby World Cup.
He was returning to Fiji last week with the aim of being involved in the IRB's Pacific Nations Cup before meeting up with his new Edinburgh team-mates for pre-season training, subject to work permit clearance.
He added: "It will be good for me to play in the Magners League and, of course, the Heineken Cup. I just want to play some decent rugby and do my best for Edinburgh."
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