Genoa have signed Gronbaek on loan from Stade Rennes with a purchase option worth €10.5m.
Gronbaek arrived at Rennes last summer when he was signed for €15 million from Bodo/Glimt, after he had taken part in turning the Norwegian club into a serious contender in the European club competitions and making his debut in the Danish national team at the same time.
Gronbaek had a bright to his career in Ligue 1 but didn't feel right at home at the environment in the French club.
Soon his performances dipped, and he began to struggle in Northern France under the leadership of first Julien Stéphan and since Jorge Sampaoli.
He then attempted to restart his career, when he was signed on loan by struggling Southampton at the bottom of the Premier League but injuries limited his involvement to five matches.
At Genoa, the former AGF-midfielder will be teammates with Danish compatriots Morten Frendrup and Sebastian Otoa.
So far, he has been capped six times for the Danish national team but he has not been selected for the national team squad since Brian Riemer was appointed in October last year.