The Croatian made 51 appearances during a loan stint with the club last term and he has been widely tipped to join on a permanent deal this summer.
While the Blues are yet to make an official announcement, the deal appears to have been completed with the midfielder expressing his delight over the switch through the app before the story was quickly taken down.
The Blues are under a transfer ban for the next 12 months but they have been permitted to secure the signing of Kovacic, given he was already registered with the club last term.
Still, the club had to finalise the deal before the transfer embargo begins on July 1 and they have done so after agreeing on a £50m sum with Los Blancos.
Kovacic may remain the only signing for the club during the summer
unless they are able to overcome or seek to freeze the ongoing embargo.