The Oak Leafers earned their place in Monday morning's draw by beating Waterford on Saturday.
Donegal enter the qualifiers after Sunday's Ulster SFC semi-final defeat by Tyrone in Clones.
Meath have home advantage against Sligo and Clare make the trip to play Laois, with the matches to be played on 1 and 2 July.
Venues, dates and throw-in times on the 2A fixtures will be confirmed later on Monday.
Derry have been drawn away against Mayo in the All-Ireland 2A qualifiers while Donegal will entertain Longford.