Former Scotland international Weir, 43, was a strong contender for the managerial vacancy at Goodison Park following the departure of Moyes last month to Manchester United after serving two years as coach under the former Toffees boss.
Everton chairman Bill Kenwright opted instead to bring in Roberto Martinez from FA Cup winners Wigan to fill the void so, armed with a glowing reference from mentor Moyes, Weir jumped at the chance when the Blades came calling. "I'm obviously happy, it's a great opportunity for me," Weir said.
"I'm very excited about it. It's a great start to my managerial career and I can't wait to get started."
Former Everton and Rangers defender Weir, appointed on Monday as permanent successor to Danny Wilson and handed a three-year contract, revealed the interview process at Goodison had been an uplifting experience.
"It was something I felt I could do and I thoroughly enjoyed the process," he said.
"I genuinely felt I had a decent chance. Bill called and told me he'd decided to go externally, which I understand his reasoning, but I came out of the interview knowing I was ready to be a manager.
"It was a great experience for me and made me realise how much I wanted it and how much I was ready for it. So overall it was completely the right thing to do.
"I've no regrets. I genuinely feel I was close, although you're better asking Bill that, it was the right thing to do and I put my heart and soul into it and when this opportunity came up I've been exactly the same.
"I'm not a person for looking back, I look forward and I'm excited to be here and looking forward to the challenge."