The competition will take place in Dublin with the first two matches being played in February and four more following in May.
The tournament will be on a league basis with the four sides playing for the 4 Associations Cup.
The tournament represents the effective re-establishment of the British Home Championship which was shelved in 1984, albeit with the Republic taking the place of England.
Scotland manager George Burley said: "We will have two games and that will be exciting. I am sure the people of the Republic will be looking forward to that and the Tartan Army will be out in force.
"All these fixtures are never easy to fit into the calendar but these dates suit everyone at the minute.
"I'm sure we'll look at it and see how it goes and if it's a success for everyone then we can try and carry it on."
George Peat, president of the Scottish Football Association, believes the tournament will capture the imagination of fans in the competing nations.
"I am absolutely delighted that the 4 Association tournament has become a reality," he said.
"When we sat down to discuss the plans, we were all excited about putting on a tournament that would celebrate the game and give our fans a great experience.
"This new event will do exactly that and we certainly look forward to taking part and, of course, hopefully winning it in 2011."
Welsh counterpart Peter Rees added: "The Football Association of Wales is delighted to be part of this celebration event in Dublin in 2011.
"We look forward to crossing swords with our two cousins from across the Irish Sea, as well as Scotland in friendly rivalry. I am sure Welsh football fans will be delighted with this news."
Irish Football Association chief executive Howard Wells expects the tournament to yield financial dividends for the home nations.
"This visionary tournament is exciting and provides all four countries with the opportunity of measuring progress in terms of international development," he said.
"For supporters it also provides a real opportunity to see first-class competition live and within easy access.
"From a commercial and tourism perspective it will provide a showcase for governments to support and market."
Chief executive of the Football Association of Ireland John Delaney said: "We are delighted to host the 4 Associations tournament.
"This will be the first time Ireland has hosted a senior international tournament and the atmosphere around Dublin will be tremendous, especially with thousands of visiting supporters from Scotland, Wales and Northern Ireland expected to travel for the matches.
"The tournament will be a fitting celebration for our fantastic new stadium (the rebuilt Lansdowne Road) which is on schedule for completion in 2010."
The English FA were not expected to sanction England's involvement in any home tournament after frequently showing little enthusiasm for such an event in recent years.
An FA spokesman said: "As there are limited international dates for opportunities to play nations from outside Europe, we like to use several dates to play teams from South America, Africa and Asia.
"Otherwise the only time we would get to play such countries is restricted to World Cups.
"We have played several fixtures against the home nations since 1999 and our preference is to play one-off games rather than a tournament - if they fit in with the manager's plans.
"Clearly friendly dates - at a premium - are important to the manager as preparation for qualifying matches and tournaments.
"Due to this, we regularly try to select opponents who will help prepare the team for the style we are likely to face."
Sporting Life.