The Coventry-born forward will now make the move back home to the Midlands and step up to the English top-flight with Warriors.
And the 30-year-old is determined to repay the faith of Hill who has finally signed him after two previous attempts.
"I'm excited and delighted about it all," said Gulliver. "I wasn't expecting the move, it came out of the blue so I'm very keen to get started and take such a big opportunity.
"I actually don't think it has really settled in yet. I don't think until the season starts I will realise I am in the Aviva Premiership. I'm humbled by the move in many ways and the chance to go up against the very best players in the world.
"When Richard (Hill) was at Bristol he came in twice for me, but I was unfortunately injured so couldn't make the move. It is third time lucky and grateful that he has kept half an eye on me.
"The chance to work with Phil Davies is also a real pull, he is such a well respected coach. I've already had a chat with him and started to nail down what he wants from me. I also spoke to Gavin Cattle and he always spoke very highly of him."
Gulliver will become the third new second row at Warriors next season as he joins fellow recruits James Percival and Chris Jones. And the hard-hitting lock is keen to impress from day one in his new surroundings.
He added: "There is new competition in the second row next season at Sixways with some new faces.
"I know Percy (James Percival) from my time at Coventry, when he was on loan, and Chris Jones has plenty of top-flight experience and real quality. But we all start from scratch and from the first day of pre-season I want to make an impression and give it a bash.
"It's also nice to be back in the Midlands and closer to the family. I've been settled down in the south over the last four years at Plymouth Albion and Cornish Pirates. I will be leaving a lot of friends, but I have to take this chance."
Gulliver was cruelly ruled out of the two-legged RFU Championship final between the Warriors and Pirates after picking up a leg injury.
However, he admits his match day duties at Sixways - when he was running water for team-mates in front of a packed house - only whetted his appetite for the move.
"It's pretty awesome at Sixways," admitted Gulliver. "The atmosphere in the second leg was immense and to be involved in that week in and week out will be special. It is not just a one-off, those Worcester Warriors fans are always loud.
"Cornish Pirates are a fantastic club and they are building something special down there. I'm sure the Worcester fans will have been impressed by what they saw over two finals this season.
"It's hard to leave as there is a really tight-knit group of us in Cornwall, but the opportunity to come to Warriors was massive and too big to pass up.
"This is huge to me and I'm very grateful to Worcester Warriors for this chance and the Pirates for their understanding."