The Republic of Ireland international was on the verge of joining Villa in 1999 from Wolves only for a late hitch over the transfer fee to see him move to Coventry instead.
But the 31-year-old has agreed to move to Villa Park until Major League Soccer restarts in March.
Villa received the final paperwork from the Galaxy giving the green light to the move during the early hours of this morning.
Keane could face an instant reunion with his Galaxy team-mate Landon Donovan in Saturday's home Premier League clash with Everton.
Donovan has linked up with the Toffees for a second loan period.
It is also a case of second time lucky for Villa boss Alex McLeish regarding the capture of Keane.
McLeish was hopeful of signing Keane 12 months ago when in charge of Birmingham, who announced they had agreed a £6million fee with Tottenham.
But the player instead went on loan to West Ham before leaving White Hart Lane for the United States last summer.
McLeish said: "We have been pursuing Robbie to bring him in with his extra experience in terms of the attack.
"I believe we could be doing with that when you see one or two of our players getting injured over the last couple of weeks.
"It does leave us a little bit short.
"We've got young kids trying to prove themselves in the Barclays Premier League but it's very scatter-gun the experience they are getting with 10 minutes here, 15 minutes there.
"I really believe we could be doing with that wee bit of experience that someone like Robbie provides."
McLeish is confident Keane can still make his mark at Premier League level and believes he will be keen to show maintain his sharpness ahead of the Euro 2012 finals with Ireland.
He said: "Robbie is a guy who is going to be playing in a huge tournament at the end of the season (Euro 2012).
"I'm sure Robbie Keane will not want to let his standards drop at this stage of his career.
"If anything, we should have a massively motivated boy on our hands."
Keane said: "I'm delighted to be back in the Premier League. This is only short term, of course, but there has been a lot of speculation over the years linking my name to Villa and, finally, I'm here.
"I'm excited about it and I know I'll really enjoy my time here. It's only for two months but I will do my absolute best in these two months.
"Villa is a great club, a club with a massive tradition and standing in the game and Villa Park is one of the finest stadiums I've ever played in.
"If selected to play on Saturday, I will genuinely be looking forward to it and I'll be excited to be involved again in Premier League action.
"I've been training with the players here for the past few days and it's been great but I'm not naive enough to think I'll just walk straight into the team.
"If I can help and contribute to the overall effort of the team then hopefully I will be of benefit to Aston Villa. That's my aim."
Villa's record signing Darren Bent, who played alongside Keane at Tottenham, said: "It's a top signing, a really clever move.
"In training Robbie has looked razor-sharp and up for the challenge. He's a great player and he has been for many years.
"There is no doubt he will give absolutely everything during his time here. He knows the game inside out and, from what I have seen of him so far, he's bright as a button.
"He will help all the other strikers here but, more importantly, he will help Villa.
"He will bring experience which will aid a few of the younger lads who are breaking through into the team and the other youngsters in and around the place."