The countries today informed Uefa in writing that they would be interested in bidding to host the Championships on a three-way basis.
So far, Turkey are the only other nation to inform Uefa they want to host the tournament, with a deadline of midnight this evening for expressions of interest.
SFA chief executive Stewart Regan today confirmed the bid for Euro 2020 was underway.
A source close to Uefa said a written expression of interest from the three 'Celtic' countries has been submitted to the European governing body.
Bidders would need to put forward up to 10 stadiums to host matches in the European Championships, which is being expanded from 16 teams to 24 from 2016.
Scotland and Wales would struggle to provide that number of stadiums to satisfy Uefa requirements, but Ireland's involvement would cover the shortfall.
The formal declaration of interest does not commit the Celtic countries to proceeding with a bid, however – a decision is not due to be taken by Uefa for 18 months.
The countries have not fared well in the past in bidding for the tournament.
Scotland and the Republic of Ireland bid jointly for Euro 2008, but were one of the first to be eliminated, and Scotland and Wales considered bidding jointly for Euro 2016 but decided against it.
Turkey's bid is in some disarray already because their FA has been engulfed by allegations of corruption and match-fixing in Turkish football, and it also conflicts with Istanbul's bid to land the Olympics in the same year.
Uefa president Michel Platini had signalled he would support Turkey's bid – but only if Istanbul failed in its bid to land the Olympics in the same year.
The Turks have formally applied to host Euro 2020, putting it in direct conflict with Istanbul's bid for the summer Olympics and Paralympics the same year.
Both Uefa president Michel Platini and International Olympic Committee (IOC) chief Jacques Rogge have warned the country would not be allowed to host both events in the same summer and should drop one or the other.
Istanbul is one of five cities in the race to host the 2020 Games, along with Baku, Doha, Madrid and Tokyo, following Rome's withdrawal.
Meanwhile, Scotland boss Craig Levein today handed Dundee United forward Johnny Russell his first call-up to the national squad for their friendly against the USA on Saturday, May 26, in Jacksonville, Florida.
Wigan's Shaun Maloney has also earned a recall.
Russell had been widely tipped for a call-up and Maloney was in impressive form toward the end of the Premier League season, grabbing the only goal of the game in a vital home win against Manchester United.
"He has had a very good season, and he's a young guy with a big future. I felt he deserved the recognition of being involved and the experience of the group will help him going forward," Levein said of Russell, who is already attracting attention from a number of clubs.
The Scots boss also dimissed any notion that the three Rangers players in the squad – Allan McGregor, Steven Whittaker and Lee Wallace, will in any way be distracted by the on-going takeover situation at Ibrox.
They could, as prospective owner Charles Green conceded yesterday, activate exit clauses in their contracts should they choose to do so.
He said: "I have every confidence that what's going on at the club will not affect them. If they are to leave, and that's a big if, then the transfer window doesn't open until June and we will be back by then."
Matt Gilks (Blackpool)
Craig Gordon (Sunderland)
Allan McGregor (Rangers)
Phil Bardsley (Sunderland)
Steven Whittaker (Rangers)
Christophe Berra (Wolves)
Gary Caldwell (Wigan)
Russell Martin (Norwich)
Charlie Mulgrew (Celtic)
Lee Wallace (Rangers)
Andy Webster (Hearts)
Barry Bannan (Aston Villa)
Scott Brown (Celtic)
Craig Bryson (Derby)
Don Cowie (Cardiff)
James McArthur (Wigan)
Matt Phillips (Blackpool)
Shaun Maloney (Wigan)
David Goodwillie (Blackburn)
Craig Mackail-Smith (Brighton)
Kenny Miller (Cardiff)
Johnny Russell (Dundee Utd)