The 48-year-old played at the highest level with Barcelona and the Netherlands, winning more than 100 caps, and won the Eredivisie title with PSV Eindhoven three times as a manager.
Cocu said last season's Championship play-off finalists Derby were the "right fit" for him.
"I realise and know in the world of football that you have to bring a level of performance -- it doesn't matter if it's the Premier League or Eredivisie (Dutch top division)," he said.
"Over the last few years the club has tried to build something and I want to continue this process, this philosophy. I have the feeling it's a good fit and a good moment to step in."
The former Fenerbahce boss said: "To develop players is very important to bring the philosophy we have -- to try to make a plan for each individual player to make it possible to make it to the first team. The first team as well need to be competitive."
Derby challenged for promotion last season, falling at the final hurdle in the play-off final at Wembley and Cocu said the club were also aiming high this season.
"We will try to get in the top six in the league but the most important thing is the football we play and the development of individual players," he said.
Derby received a big compensation fee for Lampard when his former club Chelsea appointed him as their manager earlier this month, reportedly around £4 million ($5 million).
But owner Mel Morris said the club would not abandon its principles of trying to produce its own first-team players and a "big spend" was not anticipated before the transfer window closes.