Ex-Sunderland boss Bruce, 58, resigned as Wednesday boss last week following talks with the Magpies.
He was confirmed as Newcastle boss on a three-year deal, taking coaches Steve Agnew and Stephen Clemence with him.
The Owls, whose Championship campaign starts in 10 days, have yet to name a replacement for Bruce.
In a statement, the Yorkshire club said: “Following Newcastle United’s announcement on 17 July 2019 of its appointment of former Sheffield Wednesday staff Steve Bruce, Steve Agnew and Stephen Clemence, the club confirms that it has today reported Newcastle United’s conduct to the Premier League.
“As the Premier League will now initiate and carry out investigations into the club’s allegations, the club will not be commenting further on this matter whilst such investigations are ongoing.”
Bruce was only in charge of Wednesday for 18 games after he began work in February following the departure of Jos Luhukay.
The former Manchester United defender saw his Wednesday side lose only three times after taking charge on 1 February, leading them to a 12th-place finish in the Championship.
A boyhood Magpies fan, Newcastle are the 10th club Bruce has managed and this is his 11th post, having led Wigan Athletic twice.