The 19-year-old midfielder will discuss personal terms with the Midlands club and, depending on an agreement being reached, undergo a medical on Tuesday.
It is something of a coup for Villa, who have made no secret of the need to make a number of signings before the start of the season a week on Saturday. Martin O'Neill, the manager, has had Delph in his sights for some time, but it had looked as though they would miss out, unwilling to meet Leeds' high valuation of the player.
However, when Manchester City and Tottenham registered their interest last week, Mark Hughes saying he was "a young player who has been brought to our attention", O'Neill was compelled to increase his offer.
It is understood that the way in which negotiations were conducted played a decisive role in the decision of Leeds to accept Villa's bid. In a thinly veiled dig at both City and Spurs, Leeds praised the 'honourable manner' in which Villa made their approach.
'Leeds United can confirm that a fee has been agreed with Aston Villa for Fabian Delph,' said the club in a statement posted on their official website. Leeds United wishes to place on record our appreciation for the honourable manner in which Aston Villa have conducted their interest in the player.
'The club has resisted approaches from other Premier League clubs since agreeing terms with Aston Villa. Having given Villa our commitment to transfer the player (subject to medical), we had no intention of going back on that.'
Where Delph will fit into the side, once Downing returns to fitness, is less certain. The midfielder, who was the Football League's Young Player of the Year last season, is predominantly left-sided, but he can also play in a more central role.
Meanwhile, reports have suggested that Newcastle right-back Habib Beye is being targeted as cover for Luke Young. The 31-year-old Senegal defender would cost in the region of £2.5 million.