Wing enjoyed a successful loan spell with the Millers in the second half of last term and proved a very popular member of the squad in the process.
Warne was keen on bringing Wing back to the club earlier this summer, but financial reasons scuppered the prospect of a move for the 26-year-old, who has entered the final year of his deal at parent club Middlesbrough.
Wednesday promptly beat off interest from the likes of Hull City and Luton Town to land the midfielder, who has already made his mark at Hillsborough.
Warne said: “I am absolutely fine with it. The good thing is that I know what Lewis is good at and what he is not so good at. It is not a massive problem for me.
“I always like players who risk their careers to play for us here and will always have a lot of respect and fondness for them and it is no different with Lewis.
“I will look forward to seeing him on Saturday and shaking his hand at the final whistle – and I will look forward to us keeping him quiet.
“But football is what it is. I do not fall out with anyone who shows due respect and he definitely did.
“He is a good kid and he will have a great career there, no doubt.
“But it is about what our midfielders can do and I have got three from five who I have got to pick who will hopefully cause as many problems to their midfield three as they do to ours.”
Warne has confirmed that a final ‘informed’ decision will be made this morning on the extent of Freddie Ladapo’s involvement against the Owls.
The centre forward has been suffering from tonsillitis, but trained on Thursday.