He said: "I'm very pleased to be back. It has been such a long time since my last game but I'm really looking forward to playing again. It's important for us to win this game and move up the league but it's also important for me to come through it so that I can get back into playing my best rugby in the four games we have left."
Leonelli's inclusion is one of three changes, including one positional, that coach Sean Lineen has made to the side that beat league leaders Leinster 26-20 at Hughenden last Friday. To accommodate Leonelli, Rory Lamont switches from full back to right wing while Moray Low returns in place of Euan Murray at tight-head.
Lineen said: "It's great to welcome Francisco back after five months out because he's a quality player and we've brought Moray in for Euan, who is being rested for this game. It's a great chance for both players with just four games left this season.
"This is another massive game for us as Connacht rarely lose at home. We scraped past them in November with a 39-34 win at Hughenden so we know this will be a tough match and we'll have to continue the form from last week's win over Leinster," he added.
Glasgow Warriors team to play Connacht
15 Francisco Leonelli
14 Rory Lamont
13 Graeme Morrison
12 Scott Barrow
11 Thom Evans
10 Dan Parks
9 Graeme Beveridge
1 Justin Va'a
2 Fergus Thomson*
3 Moray Low**
4 Andy Newman
5 Alastair Kellock* CAPTAIN
6 Steve Swindall
7 John Barclay*
8 John Beattie*
Substitutes
16 Scott Lawson*
17 Kevin Tkachuk
18 James Eddie
19 Andrew Wilson*
20 Donnie Macfadyen
21 Colin Gregor
22 Hefin O'Hare
* indicates player in the Scottish Institute of Sports
** indicates National Academy Player