The pair were two of eight England internationals named in the 2009 Lions party which leaves for South Africa on May 24.
Mears has been in superb form for Bath this season and has cemented his place in the England starting line up after fighting off stiff competition from the likes of Northampton's Dylan Hartley and Leicester's George Chuter.
Monye burst on to the international scene earlier this season and has not looked back since. The 26-year-old made his international debut against the Pacific Islanders in November of last year and has become a regular in Martin Johnson's first XV.
The Dream Team was chosen by three former Lions in Stuart Barnes, Dewi Morris and Will Greenwood.
Sky Sports Dream Team
15. Olly Morgan (Gloucester Rugby)
14. Joe Maddock (Bath Rugby)
13. Gonzalo Tiesi (Harlequins)
12. Seilala Mapasua (London Irish)
11. Ugo Monye (Harlequins)
10. Charlie Hodgson (Sale Sharks)
9. Paul Hodgson (London Irish)
1. Marcos Ayerza (Leicester Tigers)
2. Lee Mears (Bath Rugby)
3. Mike Ross (Harlequins)
4. Dean Schofield (Sale Sharks)
5. Ben Kay (Leicester Tigers)
6. Chris Robshaw (Harlequins)
7. Steffon Armitage (London Irish)
8. Juan-Martin Fernandez Lobbe (Sale Sharks), captain
Monye's Harlequins team-mates Chris Robshaw and Jordan Turner-Hall were voted Guinness Premiership Player of the Season and Land Rover Discovery of the Season respectively, while Richard Cockerill of Leicester Tigers picked up the award for the Hilton Director of Rugby of the Season.