There were five different Edinburgh try-scorers at BT Murrayfield, with Stuart McInally and Tim Visser each crossing over before the break.
Ben Toolis and Dougie Fife each grabbed a second-half score, while Sam Hidalgo-Clyne's try was part of a 25-point haul for the in-form scrum-half.
Standing between them and the trophy is either Gloucester or Exeter Chiefs, with the English rivals set to face off this evening in the other semi-final.
But before head coach Solomons starts plotting for that clash, he has called on the entire Edinburgh set-up to cherish their achievement so far.
"It's fantastic for everyone involved with the club, the players, coaching staff and the supporters and a great moment for Scottish rugby as a whole," he said.
"The final will be a massive game. Both Gloucester and Exeter are powerful teams. You don't find weak teams in the Premiership so we know it will be a huge challenge.
"But it's important we enjoy this moment. We are a very tight group having been through so much adversity this season and we should celebrate wining a semi-final.
"We've had a really tough season. You are always without players but we have been through so many changes that it had the effect of bringing through players."
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