Croatia captain Luka Modric said Wednesday he had penned a one-year contract with AC Milan to "stay competitive and in Europe".

"I'm happy to be here and I look forward to a new adventure," the 2018 Ballon d'Or winner told AC Milan's TV channel after joining from Real Madrid.

Modric, who turns 40 in September, joined the Spanish giants from Tottenham in 2012, going on to win six Champions Leagues, four La Liga titles and two Copa del Rey trophies.

"I wanted to stay in Europe, to continue playing competitive football. I had some other offers but when Milan showed up for me it was clear from the first moment," he said.

Milan finished a disappointing eighth in Serie A last season and will not play in European competition.

But Modric insisted Milan remain "one of the biggest clubs in Europe". 

"Milan cannot be satisfied with average and needs to have the biggest goals possible, to win titles, to compete with the best teams in the world, that's why I am here."

Modric signed a one-year contract, with an option for an additional season with the seven-time Champions League and 19-time Serie A winners.

"I'm never satisfied, I always want more," he warned. "When you've experienced that feeling (of winning), you want to feel it even more. I still have hunger, desire, still wanting more."

To explain his longevity, Modric said "the most important thing is the love for the game, for football".

"That's what I still have, what I still feel in my belly, this fire, that's what pushes me ... there is no secrets, for me it's the passion, the love for football. I am never satisfied."

The 2018 World Cup runner-up also spoke of his childhood memories of Milan.

"When I was a kid, I watched the Italian league a lot, Milan was my favourite team," he recalled. 

"Also because Zvonimir Boban was there, who was my idol," he added, referring to his compatriot who wore the Rossoneri jersey from 1992 to 2001.