Mark McHugh's side were four point winners over Cavan on Saturday.
In Round 2A, the champions of Connacht and Leinster will square off at Pearse Stadium, with Galway drawn to face Westmeath.
Cork face a long trip to Donegal, Tyrone welcome Mayo to Omagh, and Louth will host Armagh.
All-Ireland champions Kerry will make the trip to Kildare for Round Two B of the All-Ireland Senior Football Championship.
Derry will host Meath, Dublin are away to Cavan, and Monaghan will host Roscommon.
The losers of those ties will be eliminated from this year's Championship.
The winners of the Two A matches will go directly to the quarter-finals, while the losers in Two A will be paired against the winning teams from round Two B.
The second-round games will be played over the weekend of June 13th and 14th.
Westmeath Football Manager Mark McHugh is delighted with his side's character following their win over Cavan on Saturday.
The Lake County secured victory after extra time over the Ulster side as they came away with a 1-31 to 3-21 win in Cusack Park.
Kevin O'Sullivan's goal pushed his side towards victory, with Brandon Kelly, Senan Baker and Sam McCartan also impressing.
Westmeath will now face Galway away from home in round 2A.
McHugh says it took a huge effort to get over the line:
Mark McHugh spoke to the media after the game:
Coverage of Westmeath vs Cavan was with thanks to Total Tile & Bathroom Centre Mullingar.
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