The Ulster champions will face provincial rivals Monaghan and Donegal in the group stages of the new-look All-Ireland Senior Football Championship.
Derry or Armagh, who contest the Ulster final on 14 May, will drop into Group Four with Monaghan, Donegal and the Munster runners-up (Kerry or Clare).
Tyrone have been drawn alongside the Ulster runners-up in Group Two.
In the Tailteann Cup, Fermanagh and Antrim are both in Group Four.
The All-Ireland group stages get under way on 20/21 May with matches featuring the Connacht and Munster winners and runners-up.
The following week (27/28 May) sees the Leinster and Ulster winners and runners-up contest their group openers.
In the All-Ireland round-robin series, National League champions Mayo have been drawn alongside Cork and the Munster winners and Leinster runners-up in Group One.
That raises the mouthwatering prospect that reigning champions Kerry, Dublin and Mayo – three of Gaelic football’s powerhouses – could meet in the same group if Kerry beat Clare as expected in the Munster decider and Dublin lose to Louth in the Leinster final.
Group Four will be dominated by Ulster and would see a repeat of last year’s Ulster final between Derry and Donegal if the Oak Leafers beat Armagh at Clones on 14 May.
Tyrone, the 2021 All-Ireland champions, await the Ulster runners-up in Group Two, meaning the Red Hands could face bitter rivals Armagh or Derry, who they haven’t faced since last year’s Ulster quarter-final.
If Galway win the Connacht title, they are destined for a rematch with either Armagh or Derry, who they beat in the All-Ireland quarters and semis respectively last year.
Westmeath, who qualified for the All-Ireland by winning last year’s Tailteann Cup, are also in Tyrone’s group.
Group Three will feature the Leinster winners (Dublin or Louth), the Connacht runners-up (Galway or Sligo), Roscommon and Kildare, who ran Dublin close in Sunday’s Leinster semi-final.
How does it work?
The restructured All-Ireland series sees 16 counties drawn into four groups of four, comprised of the eight provincial finalists, the seven next highest-ranked teams based on league position and last year’s Tailteann Cup winners (Westmeath).
Each team will play one game at home, one away and one at a neutral venue. The provincial winners (top seeds) will have home advantage in round one against a third seed while the second seeds will be at home to the fourth seeds.
Only one team will be eliminated from each group. The four group winners advance to the All-Ireland quarter-finals while the eight teams who finish second and third will face each other in preliminary quarter-finals.
All-Ireland draw in full
Group One: Kerry/Clare winners, Dublin/Louth losers, Mayo, Cork
Group Two: Galway/Sligo winners, Armagh/Derry losers, Tyrone, Westmeath
Group Three: Dublin/Louth winners, Galway/Sligo losers, Roscommon, Kildare
Group Four: Armagh/Derry winners, Kerry/Clare losers, Monaghan, Donegal
In the Tailteann Cup, last year’s beaten finalists Cavan have been drawn alongside Offaly, Laois and London in Group One, while Down face Meath, Tipperary and Waterford in Group Two.
Fermanagh, who were promoted from Division Three alongside Cavan earlier this year, face Ulster rivals Antrim, Wexford and Leitrim in Group Four.
The Tailteann Cup begins on the weekend of 13/14 May. The four group winners advance to the last eight while the four second-placed teams will face the three best third-placed counties or New York in the preliminary quarter-finals.
Tailteann Cup draw in full
Group One: Cavan, Offaly, Laois, London
Group Two: Meath, Down, Tipperary, Waterford
Group Three: Limerick, Wicklow, Longford, Carlow
Group Four: Fermanagh, Antrim, Wexford, Leitrim