Warburton took charge of his first competitive game at Ibrox as Rangers eased past Peterhead 3-0 in the League Cup on Sunday.
And the former Brentford boss believes the win bodes well for Rangers’ upcoming promotion bid, which will begin with the Championship opener against St Mirren on Friday.
“Today was game five of five (pre-season fixtures) and I’m delighted with the way it’s gone,“ Warburton said.
“It was a good result (against Hibernian in the Petrofac Training Cup) last week and again today, so we’re ready for Friday night.
“I’ve looked at the team, the squad is all fit and ready and we’re in good shape, touch wood.”
Rangers continue to be linked with Hibs’ playmaker Scott Allan, as well as former Derby midfielder John Eustace, but Warburton insists he is already satisfied with his squad ahead of the new league campaign.
“I’m pleased with how we are looking. From day one the whole squad has surprised me with their work ethic, application and quality, which has been outstanding,” he said.
However, while Warburton again refused to be drawn on speculation surrounding Allan, he admitted that Rangers are still looking to strengthen.
“It would be disrespectful for me to talk about Scott Allan. It is a saga because he’s not my player. Of course he is a talented player but he’s a Hibs player and it’s not for me to talk about another club’s player.”
“We are always looking (to add players). We have to. A club like Rangers always has to be looking to add quality,” added Warburton.
“If the right player becomes available, then we always have to be looking (to make an approach). If we don’t then we are going to fall behind very quickly.”
Meanwhile, Peterhead boss Jim McInally bemoaned the way in which his side conceded two late goals in their attempts to find an equaliser against Rangers on Sunday.
“I totally exposed the boys in the second half by putting guys up the park trying to score,” he said. “We made it a more entertaining match for people with the kamikaze way that we played.”