The tournament had previously been dominated totally by English sides up till now.
The students, who finished third in Scotland's men's Premiership and lifted the British Universities and Colleges (BUCS) Vase, celebrated wildly at the final whistle.
Winning promotion was their No 1 aim, according to player/coach Hamish Imrie who praised his men from bouncing back from a confidence-sapping 3-2 Scottish Cup semi-final defeat by Hillhead on Sunday and the hammer blow of losing out on promotion at the first attempt last week, being edged by Oxford 4-1 after penalty strokes.
Scottish international Imrie, who took over the coaching role at the start of the season, said: "We've had over 40 games in BUCS and the Premiership this season and the boys have given me everything they have.
"To become the first Scottish university to play in the same league as the elite of British university hockey is a great achievement, particularly after the disappointment of last week when we were beaten in a penalty shootout after Oxford levelled at 2-2 late in the game."
Next year, the students will travel to venues like Exeter, Nottingham and Birmingham, but and Imrie will start planning in the next few days, but he added: "Let's enjoy the moment."
Edinburgh attacked from the first whistle, pressing Oxford Brookes back, trying to capitalise on the English side's decision to travel up by bus on the morning of the game, leaving Oxford at 5.40am.
Declan Bradley from Birmingham opened Edinburgh's account after 12 minutes and Inverness-born Iain McFadden added No 2 two minutes later. Skipper Robbie Croll netted from a drag flick just before the half time whistle.
The visitors scored on a counter-attack then withdrew goalkeeper Chapman five minutes from time to have 11 outfield players. but the gamble failed when Cyprus-born Costas Stylianou fired home from close range in the dying minutes.