A Good Omens fan, who did not wish to be named, managed to snap a pic of Tennant while out on a walk.
They said: “I had heard from a friend that there was a film crew outside Fettes and when I took a walk to see what was going on, one of the security team at Inverleith park confirmed that they were filming Good Omens.
" I did ask if Michael and David were there but they denied it, saying that it was only some background second team they were filming using green screen and the trees overlooking the pond. I carried on around the pond and up to the rugby pitches, where the crew could be seen close to East Fettes Avenue.
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"I just wandered across and took a few shots of what I thought was a stand-in but it was only when I got home that I realised not only was this the case but in one shot it was clearly David Tennant (Crowley)”.
The Amazon hit series also stars Welsh actor Michael Sheen, however, he was not seen to be filming at the location.
Good Omens, based on the book by Neil Gaiman and Terry Pratchett, is on its second season, parts of which are currently being filmed in Scotland.
The series will once again be directed by Scottish film and TV director Douglas Mackinnon who has expressed his delight at filming in his home country again.