Mayo will meet Tipperary in Round 2 of the All-Ireland SFC Qualifiers while Tyrone travel to surprise package Carlow.
Tipp, who were beaten by Cork in Munster, will host a Mayo side that bounced back against Limerick last weekend, in what is a rematch of the 2016 All-Ireland semi-final.
Carlow will need to put the disappointment of provincial last-four defeat to Laois behind them quickly ahead of the visit of Tyrone, who edged out Meath after extra-time on Saturday.
There are all-Ulster and all-Leinster clashes in Cavan v Down and Longford v Kildare.
The pitch at Breffni Park is being relaid so the Cavan-Down clash is expected to take place at a neutral venue, most likely Clones.
Elsewhere, Offaly host Clare, Sligo take on Armagh, Leitrim face Louth and Waterford's questionable reward for a first Championship win since 2011 is to meet Monaghan.
"Tipperary are a very strong team," said Mayo star Tom Parsons, who is out for the season with a knee injury.
"They did very well in Division 2 and were probably unlucky not to get promoted.
"They would have been disappointed with their performance against Cork but it was (only) a week after playing Waterford.
"They're going to be a very big challenge for us. It's a tough draw."
The draw, pitting eight round 1 winners against the eight beaten provincial semi-finalists, was made on RTÉ Radio 1's Morning Ireland today by Parsons and GAA president John Horan.
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 23/24 with the Central Competitions Control Committee meeting to confirm venues and times later today.
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.