The back-row replaces John Barclay – who drops to the bench – in the only alteration to the starting XV that claimed a valuable away win against Scarlets last weekend.
Ahead of this weekend’s highly anticipated Conference B encounter, Head Coach Richard Cockerill, said: “We’ve got to win. It’s the same as last week. If we don’t, we’re relying on other results and miracles. We’ve just got to keep winning.
“Although Ulster were beaten by Glasgow, they were extremely good against Leinster the week before and they should have won. They’ve had a tough run in. They played in Dublin, Glasgow and now they come to us.
“We’ll put out our best team and we’ll both go as hard as we can to try and win. They’ve got a lot of quality, but we’ve got some pretty good players too.”
An unchanged back-three sees Darcy Graham make his third consecutive start at fullback, with Duhan van der Merwe and Damien Hoyland named on the wings.
Matt Scott – who grabbed his second try of the season in the win over Scarlets – is partnered by Mark Bennett in midfield, while last weekend’s man of the match, Jaco van der Walt, once again links up with scrum-half Henry Pyrgos at half-back.
An unaltered front-row sees captain Stuart McInally pack down alongside props Pierre Schoeman and WP Nel, with experienced lock pairing Grant Gilchrist and Ben Toolis once again selected in the second-row.
The inclusion of Bradbury is the only alteration to an otherwise unchanged back-row as Hamish Watson and Fijian internationalist Viliame Mata complete the pack.
Elsewhere, club centurion and Scotland’s record cap holder Ross Ford is named among the replacements and if involved will make what could be his last appearance at BT Murrayfield after it was announced this week that the hooker will leave the club at the end of the season.
Edinburgh team to face Ulster at BT Murrayfield in the Guinness PRO14 on Friday 12 April (kick-off 7.35pm) – live on Premier Sports
15. Darcy Graham (22)
14. Damien Hoyland (62)
13. Mark Bennett (18)
12. Matt Scott (82)
11. Duhan van der Merwe (39)
10. Jaco van der Walt (38)
9. Henry Pyrgos (22)
1. Pierre Schoeman (21)
2. Stuart McInally (135) CAPTAIN
3. WP Nel (132)
4. Ben Toolis (108)
5. Grant Gilchrist (135)
6. Magnus Bradbury (63)
7. Hamish Watson (98)
8. Viliame Mata (58)
Replacements; 16. Ross Ford (197); 17. Allan Dell (59); 18. Simon Berghan (65); 19. Callum Hunter-Hill (16); 20. John Barclay (3); 21. Charlie Shiel (4); 22. Simon Hickey (17); 23. George Taylor (3)