The striker has been allowed to leave his duties with Finland early to complete the deal, thought to involve an initial fee of around £3.5m.
This will bring Everton's pre season spending to £7m already.
The 24 year old striker is available at a reduced fee following his knee injury last year, so it remains to be seen whether he will pass a medical. Everton have fought off interest from Birmingham City, with whom Forsell has spent the last two years on loan.