The Football Association of Wales later confirmed that they will hold a press conference at 2pm, where Speed's appointment will be announced.
Speed met with representatives of the FAW on Monday to discuss the position vacated by John Toshack in September after being granted permission by Sheffield United.
All over: Gary Speed's final game with Sheffield United was the defeat at Barnsley
The talks with Wales' most-capped outfield player are expected to be a formality, with an official announcement due tomorrow after a meeting of the FAW's 28-man ruling council in Cardiff.
Although Speed has been heavily linked with the job over the past few days, the FAW's move for the 41-year-old is still a surprise.
Despite a superb playing career spanning 20 years, which included spells with Leeds, Everton, Newcastle and Bolton before ending up at Bramall Lane, Speed has struggled on his managerial debut.
After sacking Kevin Blackwell just threegames into this season, the Blades board appointed from within, ignoring Speed's obvious lack of experience, even though he had taken up a coaching role.
Out of luck: Chris Coleman
United have lost half of Speed's 18 games in charge, leaving them one point and two places above the npower Championship relegation zone.
Yet Speed has seemingly emerged as the preferred candidate ahead of Chris Coleman, despite his more considerable managerial experience, in particular with Fulham in the Barclays Premier League.
It is understood Coleman has also been offered a job at Larissa, currently bottom of the Greek Super League, although his preferred choice is naturally to manage his country.
But it is former Wales captain Speed, with 85 caps to his name, who has become the frontrunner ahead of Coleman, John Hartson, Brian Flynn and Swede Lars Lagerback, who were all interviewed last week.
Despite the prospect of managing talented youngsters such as Gareth Bale and Aaron Ramsey, Speeds faces a tough task resurrecting his country's fortunes.
Wales are currently bottom of their qualifying group for the 2012 European Championships after losing all three matches in Montenegro and Switzerland and at home to Bulgaria. It does not get any easier either, with Wales' next competitive game against England at the Millennium Stadium on March 26.
Speed's exit, on an apparent three-and-a-half-year contract with the FAW, naturally leaves Sheffield United in limbo ahead of the hectic Christmas and New Year period.
Early candidates for the post include former Hull boss Phil Brown and Chris Hughton, remarkably axed last week by Newcastle, while Coleman may also come into consideration if he does not take the job with Larissa.
Wales set to unveil Speed as boss after Sheffield United agree releaseEXCLUSIVE: Speed to be named new Wales manager imminently
Explore more:People: Chris Hughton, Kevin Blackwell, Chris Coleman, Gary Speed, John Toshack, John Hartson, Brian Flynn, Gareth Bale, Phil Brown Places: Leeds, Newcastle, Cardiff, Bolton, Wales, Montenegro, Bulgaria, United Kingdom, Switzerland Organisations: Football Association of Wales