The other last eight ties will see Kerry host Meath, Cork will face Waterford and Armagh will play Mayo.
Armagh, Kerry, Cork and Dublin will have home advantage for the quarter-finals, which will be played on the weekend of Saturday/Sunday July 6/7.
Earlier today Waterford, Galway and Meath confirmed their quarter-final slots, with Dublin’s victory over Kildare ensuring that they finished ahead of Mayo on top of Group 4.
Before today’s ties, Armagh, Kerry and Cork had been confirmed as winners in their respective groups.
In Group 1, Marion Farrelly, Emma Duggan and Meadhbh Byrne led the way as Meath did enough to see off Tipperary by 2-15 to 2-12 in Navan, Ashling Moloney scored 0-9, six of them from play, but it was not enough to save Tipperary.
In Group 2, a first-half goal from Eve Power was decisive as Waterford booked their place in the last eight with a 1-10 to 0-7 victory over Donegal at Walsh Park.
And in Group 3, Galway went on a scoring spree as they ousted Laois by 7-22 to 1-5 in Ballinasloe with Olivia Divilly and Ailbhe Davoren both getting two goals to ensure progress in second place behind table-toppers Cork.
Dublin also had a comfortable win with Hannah Tyrrell scoring a hat-trick as they defeated Kildare by 4-19 to 0-9 at Manguard Park.
In the TG4 All-Ireland SFC semi-finals, to be played at Glenisk O’Connor Park in Tullamore on Saturday July 20, the winner of quarter-final between Kerry and Meath will play the winner of the last eight meeting between Armagh and Mayo.
On the other side of the draw, the victors of the clash between Dublin and Galway will play the winners of Cork and Waterford in the other semi-final.
Meanwhile, in the TG4 All-Ireland Junior Championship, Fermanagh ended Carlow’s 100pc record when they made the trip to Netwatch Cullen Park a winning one, coming out on top by 1-16 to 3-4.
Also in Group A, Sligo defeated London by 1-20 to 5-3 when the sides met in Ruislip on Saturday evening.
TG4 All-Ireland Senior Championship
Group 1 – Meath 2-15 Tipperary 2-12
Group 2 – Waterford 1-10 Donegal 0-7
Group 3 – Galway 7-22 Laois 1-5
Group 4 – Dublin 4-19 Kildare 0-9
TG4 All-Ireland Junior Championship – Group A
Sligo 1-20 London 5-3
Fermanagh 1-16 Carlow 3-4
TG4 All-Ireland Senior Championship draw
First team named with home advantage – ties to be played on weekend of Saturday/Sunday July 6/7
1. Kerry v Meath
2. Cork v Waterford
3. Armagh v Mayo
4. Dublin v Galway
Semi-final draw
Winner QF 1 v winner QF 3
Winner QF 2 v winner QF 4
Semi-finals to be played at Glenisk O’Connor Park, Tullamore, on Saturday July 20