The 30-year-old former Scotland Under-21 captain, who launched his career with Boroughmuir and Watsionians, spent eight years in the English Championship with Bedford, Doncaster and Rotherham before moving to London and the Premiership last summer.
Cochrane said: "I'm an Edinburgh boy so it's great to fulfil a lifelong ambition to play for the team [in the place] where I was born and grew up.
"It's taken nine hard years of graft to prove my worth. I never gave up on earning a return to Edinburgh and I'm really excited to join. Wasps helped me prove that I was capable of playing at that level, so when Edinburgh came knocking at the door it was a dream come true."
Solomons, Edinburgh's head coach, can now boast considerable depth at No.2, being able to call on the services of Ross Ford, the Scotland hooker, Aleki Lutui, James Hilterbrand and Steven Lawrie, while Stuart McInally is on loan at Bristol.
He complimented Cochrane on his fortitude: "What's important here is that we have a good Scottish player who has gone away and done it the tough, hard way. We've kept a very close eye on Neil, who's got talent.
"It's great to bring a player who's from the region back into the fold. He's exceptionally committed to coming here. A guy like that will be massively motivated and I think will add a lot of value to our side."
Cochrane, who has represented Scotland at under-21, under-19 and under-18 levels, as well as turning out for the national sevens side, made a positional switch from back row to hooker mid-career, will arrive in the summer as part of the club's ongoing policy of acting early in their efforts to build a formidable squad for the forthcoming campaign.
Edinburgh's Pro12 rivals Ospreys have persuaded Alun-Wyn Jones, the British and Irish Lions prop, to reject overtures from big-spending French clubs as well as the offer of a central contract with the Welsh Rugby Union to sign a regional contract which will keep him at the club until at least after next year's World Cup.