Tyrone will meet Meath in the pick of the Round 1 All-Ireland SFC Qualifiers.
Last year's semi-finalists were eliminated from Ulster by Monaghan and will travel to Navan to face a Meath side beaten by Longford yesterday.
Kildare, stunned by Division 4 Carlow at the weekend, will head north to face a Derry team beaten by Donegal.
The 2017 All-Ireland runners-up Mayo, who were beaten for the third year in a row in Connacht by Galway, have a trip to Limerick.
Elsewhere, Louth travel to London, Wicklow host Cavan, and Offaly have a chance to put recent managerial turmoil behind them at home to Antrim.
Westmeath welcome Armagh back to Cusack Park for a rematch of a Division 3 tie won by the Ulster side and Wexford square up to Waterford.
The draw, involving the 16 teams eliminated before the provincial semi-final stage, was made on RTÉ Radio 1's Morning Ireland today by former Kerry star Colm Cooper and the GAA's head of games administration and player welfare Feargal McGill.
Teams that played in Division 3 or 4 of the Allianz Football League this season were given home advantage against Division 1 or 2 teams.
The games will be played on the weekend of June 9/10 with the Central Competitions Control Committee meeting to confirm venues and times tomorrow.
For the first time, all games will be decided on the day, with a free-taking competition used to separate team who finish level after two separate periods of extra-time.