Lundstram was unveiled as a Rangers player earlier this week, signing a three-year deal after his contract at Bramall Lane officially expired.
The midfielder revealed that Blades teammate John Fleck, a Rangers fan and former player, “played a massive part” in his move north of the border.
And another former teammate, Scottish international striker McBurnie, admitted he had advised “natural born winner” Lundstram that the next chapter of his career should come at Ibrox.
Sheffield Wednesday injury update on Michael Smith, concerns cooled over defensive pair
Sheffield Wednesday's crucial Lee Gregory update as new signing is ruled out 'for some time'
"They sat behind the ball" - Sunderland boss talks Sheffield Wednesday tactics after Owls win in Carabao Cup
‘One or two wilted’ – Sheffield Wednesday to learn from last year as Darren Moore makes brutally honest transfer admission
Sheffield Wednesday identify two possible striker transfers – meeting to be held to discuss next steps
“He’s a top player. John can play anywhere in midfield,”McBurnie, speaking to the Rangers blog Four Lads Had A Dream, said.
“He’s a midfield engine, excellent with both feet and has a great range of passing with an eye for a goal as well.
“He’s a natural born winner. As a lad from Liverpool, I think we all know what they are like, passion wise. Demanding of his teammates both in training and in games, but one of the best blokes you will meet.
“He will be a big miss in the Sheffield United dressing room.”
Lundstram turned down a contract offer to stay at Bramall Lane, which then-Blades boss Chris Wilder claimed would have put him in the bracket of the top earners at United.
Instead, Lundstram ran his contract down last season as the Blades were relegated to the Championship.
Asked how much he was looking forward to seeing Lundstram in a blue shirt McBurnie admitted: “Very much. He had mentioned the interest to me a while back and I’ve been persuading him every day since (once it was known he was leaving Sheffield United).
“That’s how highly I rate him. To be fair he didn’t need much persuasion because I think as soon as he spoke to the manger and realised how big the club was, he was sold.
“So I’m looking forward to watching him play for the teddies.”