Villa, who have been insisting that Downing was going nowhere, caved in when the winger told them he was desperate to move to Merseyside.
They have offered Wigan ?9million for Charles N'Zogbia as a direct replacement and hope to tie up the deal on Thursday as well.
Down and out: Aston Villa winger Stewart Downing has finally sealed the move he wanted to Liverpool
Liverpool boss Kenny Dalglish said: 'We have been given permission to speak to the player.
'We will now try to agree personal terms with him, but it will all depend on the medical. It is a work in progress and we will see what happens and keep you informed.'
Downing, 26, was player of the season last year but rocked the club while on England duty when he announced he wanted to quit despite the fact he had two years of his contract remaining.
Villa's official stance was that Downing would be going nowhere and they rejected a ?15million offer last week. However, owner Randy Lerner - not for the first time - has done a massive u-turn.
That's the way to impress Kenny: Villa's player of the year Downing scored against Liverpool in May
And that will spark further unrest among Villa fans, who are questioning the American's ambition following the sale of Ashley Young to Manchester United as well.
Downing cost ?12million from Middlesbrough and had done little to live up to that price tag until last season. He was offered a new deal towards the end of the season but had already learned of Liverpool's interest and decided that he wanted to join the Kenny Dalglish revolution.
New boy: Liverpool have already splashed out ?9m on Charlie Adam this summer
New Villa manager Alex McLeish was told that Downing would be his player this season but has discovered that the goalposts have moved.
However, McLeish has a ready-made replacement in N'Zogbia, who nearly joined him at Birmingham a year ago. The wages were a stumbling block then but there should be no problem this time with Villa banking the Downing cash.
Ready-made replacement: Wigan winger Charles N'Zogbia (left) is now wanted at Villa
Villa chief executive Paul Faulkner confirmed: 'We have reached an agreement with Liverpool following an improved offer received earlier today and the submission of a formal transfer request by Stewart Downing.
'We believe there are replacements available in the market who can strengthen our squad ahead of the coming season.'
Villa also hope to conclude the signing of Shay Given from Manchester City in the next 48 hours.
Spree: England Under 21 midfielder Jordan Henderson (left) has also joined for ?16m from Sunderland
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Source: Daily Mail
Source: Daily Mail