Rashford was frozen out by Ruben Amorim at Manchester United and was told he would not play for the club.
Villa have agreed to pay at least 75 per cent of his £350,000-a-week wages, but that could rise to 90 per cent with performance related bonuses.
Unai Emery's side could then make the loan permanent in the summer for £40million.
Rashford has attracted interest from all over Europe in the January window after his struggles in Manchester this campaign.
AC Milan, Barcelona and Borussia Dortmund were said to be interested, but Rashford's wages presented a key stumbling block.
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Rashford's last appearance for the Red Devils was a Europa League fixture against Viktoria Plzen on December 12.
The 60-cap England international has been frozen out by Red Devils boss Amorim following his admission in December he was 'ready for a new challenge.'
Amorim has been especially critical of what he believed to be a lack of effort from Rashford on the training ground.
The United boss even claimed he would rather have Jorge Vital, his 63-year-old goalkeeper coach, on the bench over Rashford, who he said 'doesn't give the maximum every day'.
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"Imagine a talent like Rashford, our team should be so much better with him - but he has to change," Amorim said.
"If he changes, we are more than welcome [to include him] - and we need it. But in this moment we have to set some standards. We are waiting for Rashford, if he wants it really bad.
"You [the media] want to make it personal, I have nothing against Marcus, but I have to make the same rules for everybody.
"We need goals, we need [players who can go] one against one, we need threat in the final third."