They will continue to work alongside Solomons for at least the next two years and there is still work to do this year, with Edinburgh gunning for a top-six Guinness PRO12 finish.
Former hooker Scott earned 11 caps for his country in a five-year international career and appeared 99 times for Edinburgh before joining their coaching staff in 2013.
And he said: "I think the club's taken massive strides forward since I've been part of it, both as a player and a coach.
"There's been a big emphasis on set piece and I see our scrum coming on really well. It was great to see our front row going into the Six Nations and performing well.
"I'm really proud of what we all, as a team, have done but we still have a long way to go."
Retired fly-half Hodge racked up more than 150 Edinburgh appearances in his playing career as well as 26 for Scotland, and was a member of his country's back room team during their World Cup campaign last year.
He said: "It's a massive thing for me to coach at my home side. I've spent large parts of my life in Edinburgh and it's great to be able to influence what's going on at the club.
"We're evolving as a team and this is a great chance to develop some of the young players here, especially the backs."
Wilkins spent time coaching the Queensland Reds in Australia before moving back to the northern hemisphere with Edinburgh at the start of this season.
He said: "I'm really pleased to be extending my contract, to be able to continue the work we've started here. I've enjoyed my first season here immensely.
"It's certainly a longer season than I was used to in the southern hemisphere but that was part of the appeal - to be able to work through the ebbs and flows, to continue to improve and tweak the systems - I've really enjoyed that process."
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