England skipper Alastair Cook added an unbeaten 35 to his first-innings 105 as the home side cruised home on 94-0.
However, partner Nick Browne played the senior role with an unbeaten 55.
Browne, Essex's leading Championship run-scorer last summer, hit nine fours, the last to end the game after earlier being dropped by Ian Cockbain at point.
Essex opener Alastair Cook: "It's great to start the season well. We'd have gone into this game as favourites. That doesn't always count for much, but to dominate all the days is a pleasing start.
"It's the start of a new era here and it's a great way to start, to win by 10 wickets - but 15 more games to go.
"The slight difference for Essex now is that if we had to put out a second team, we'd manage to have a good bowling attack. Four or five bowlers who missed out in this game could easily come and fit in."
"Next week away from home at the favourites (Sussex) will be a good marker."
Nick Gledhill, BBC Essex: "Browne showed glimpses of last season's form with nine fours in his 55, while Cook followed his first-innings century with an unbeaten 35.
"Jack Taylor continued to impress with his off spin and was unfortunate not to have Cook stumped. Gloucestershire, though, were too reliant in this match on Taylor and captain Gareth Roderick.
"Essex appear to have a well-balanced side for early-season conditions. They can build real momentum should they beat pre-season favourites Sussex at Hove next week."
Essex registered the first County Championship win of 2016 as they beat Gloucestershire by 10 wickets on the final morning at Chelmsford.