The England under-21 international spoke with Premier League sides Bolton Wanderers, West Ham United and Sunderland before moving to Newcastle, signing a four-year contract worth £5.5million, according to The Mirror.
The 20-year-old was permitted to leave the Toffees for free thanks to an administrative error by the club. Everton offered Gosling a new deal verbally but did not provide him a written offer before the Premier League deadline.
Gosling was set to make about £15,000-a-week with the Toffees but will earn £25,000-a-week with Newcastle because his new team did not have to pay a transfer fee for the midfielder.
Of the clubs interested, only Newcastle committed to sign Gosling even if they would have to pay a fee after an appeal from Everton.
Chris Hughton's side went forward with the deal even though the midfield starlet will miss the first three months of the season after undergoing knee surgery.
As yet there is no official confirmation from Newcastle that a deal has been reached, although such an announcement appears to be imminent.