The 27-year-old joined Edinburgh from Northampton Saints in 2002 and has since become the club's record try scorer in the Magners League with 25 touchdowns.
But Webster says he is targeting even more career milestones in the future with Edinburgh and thanked the fans for playing such an important part in his development.
Webster said: "It is great to have reached the 100 appearance mark with Edinburgh, but I still want to achieve so much more with the club.
"I missed the first five games of the season through injury, so I'm hoping to help Edinburgh climb higher up the Magners League table and in our Heineken Cup Pool.
"I've thoroughly enjoyed my time with Edinburgh and the fans have always been brilliant with me.
"Ospreys have one of the strongest squads in the division, so we understand the sheer magnitude of the task ahead.
"But I will be aiming for a double celebration on Friday; making my 100th appearance and playing my part in an Edinburgh win."
Webster is one of seven players named in Edinburgh's team who started for Scotland against Canada at Pittodrie on Saturday, including captain Mike Blair.
Head coach Andy Robinson says he had no hesitation in selecting the club's international contingent for the visit of the 2007 Magners League champions.
Robinson said: "We are delighted to be able to welcome back our Scotland players for the match and the way they all performed over the Autumn Tests bodes well for Edinburgh.
"We have three important matches (the Heineken Cup double-header against London Wasps) over the next three weeks and it is important that every member of the squad is ready for the challenge ahead."
Scotland lock Jim Hamilton is the only internationalist rested for the match with Craig Hamilton and Ben Gissing filling the second row slots.
Meanwhile, Ross Rennie is set to make his first start for Edinburgh since March after successfully recovering from a knee injury.
The 22-year-old flanker reclaims the number seven jersey after featuring as a replacement at Connacht in October with Alan MacDonald switching across to blindside.
Edinburgh Rugby Club squad to play Ospreys in the Magners League at Murrayfield (Friday 28 November, kick off 7.30pm)
15 Chris Paterson
14 Mark Robertson
13 Ben Cairns
12 Nick De Luca
11 Simon Webster
10 Phil Godman
9 Mike Blair (captain)
1 Allan Jacobsen
2 Ross Ford
3 Geoff Cross
4 Craig Hamilton
5 Ben Gissing
6 Alan MacDonald
7 Ross Rennie
8 Allister Hogg
Substitutes: Andrew Kelly, Gavin Kerr, Matt Mustchin, Scott Newlands, Greig Laidlaw, David Blair, Hugo Southwell.
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