Chelsea were able to complete the signing despite a 12-month transfer ban imposed by world ruling body Federation Internationale de Football Association because Kovacic was registered to the club last season.
It could prove their only permanent deal of the summer if they're unable to get the ban overturned.
Although Kovacic produced some slightly irregular form during his first season at Stamford Bridge, his signing will ensure Chelsea have midfield cover as England global Ruben Loftus-Cheek recovers from a ruptured Achilles tendon which he suffered at the end of last season.
The ban states Chelsea aren't allowed to register new players for two transfer windows.
"He already possesses extensive experience at club and global level and we are sure he will be a big success with Chelsea over the next five years".
US Senate Approves Funds to Address Border Crisis
The funding is urgently needed to prevent the humanitarian emergency on the U.S. -Mexico border from worsening. The White House was prepared to veto the House Democrats' changes, administration officials said.
PSG make Neymar transfer decision•••Guardiola expresses doubt
La Liga president Javier Tebas has said he would rather Neymar does not return to La Liga if he can not improve his behaviour. It would be a win-win situation for both clubs as it would pave the way for Neymar to make his much-wanted return to Spain .