The 19-year-old midfielder was revealed to have agreed a pre-contract deal with Celtic during a press conference with now departed manager Neil Lennon on February 16.
"We’ve completed a deal for Liam Shaw, he’s signed a pre-contract. So, that’s done and we’re looking ahead", Lennon said prior to parting ways with the Glasgow side last month.
Wednesday have now confirmed the move, with the player set to move to Glasgow on July 1, but the English Championship side have launched an investigation after claiming that Celtic have broken off communication with them.
A club statement read: "Sheffield Wednesday can confirm that midfielder Liam Shaw has signed a pre-contract agreement with Scottish Premiership side Celtic.
"We are currently investigating this matter and will consider if there are any further steps available to protect the club’s interest.
"It was not our intention to place this development into the public domain out of respect to all parties concerned.
"However, we were contacted by Celtic informing the club of their intention to formally confirm this development, which was revealed by the former Celtic manager in a media briefing.
"Both clubs exchanged statements in advance of a coordinated release but Celtic have since ceased correspondence to this end.
"Shaw remains a Sheffield Wednesday player until the expiry of his current contract and will be available for selection for the remainder of the season.
"We will make no further comment at this time."
Shaw, a boyhood supporter of Wednesday and a product of the club’s academy he joined at eight, made the breakthrough at the Hillsborough club last summer.
Considered one of the most promising players to graduate through the ranks at Wednesday in recent times, his made his senior debut in July, towards the delayed end of last season.
The 6ft 2in performer has made 18 appearances this season, 14 as a starter, scoring once and having been sent off twice. Although mainly utilised in the centre of the pitch, he has had a smattering of outings at centre-back.