Warriors have also made the move to Scotstoun although first up they face a trip to Ravenhill to play Ulster in their RaboDirect PRO12 opener next Friday before welcoming Scarlets to their new home on September 7.
But after their agonising defeat in May, Kellock believes Glasgow are now ready to beat the very best.
"As a squad I've never seen us stronger," said Kellock. "Last year was built on the fact that our squad had got stronger and it's exactly the same this year. We're in a very good place.
"I like to think that teams like Leinster can be challenged - I like to think they were pretty well challenged in last year's semi-final.
"We brought the consistency into our game and we aspire to be able to stay at the top like Leinster do across the competitions but we're focused on getting a good start to the league and taking it from there.
"Our budgets have increased and at training you can see there is more competition for places and the new players coming in have impressed and showed their quality in pre-season.
"We want to do better than last year. If you had said that we would have got to the semis last year and been disappointed then we would have taken that but there are reasons why we think we can improve.
"It will be incredibly hard because there are a lot of good teams but we're in a good place and we're confident.
"We've added players with a lot of experience because we've always had a relatively young squad but they have developed into senior established players.
"The biggest improvement that has been made over the summer is the balance of the youth and the experience.
"To have everything in one place in Scotstoun is fantastic but the biggest thing is that it will be Glasgow Warriors rugby club and the more we make of it the better."
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