The pace-bowler endured a tough end to 2012, having had to contend with a heel injury as his performances during the Test tour of India were criticised.
However, despite the setbacks, Cook has insisted that 26-year-old will remain a "massive player" for his country.
"He will be very important to England. It's great to see him back playing," he told Sky Sports News. "It was a tough tour of India, more trying to get him on the park really - he had a few niggles and trying to play through the niggles didn't really work for him.
"It is great that he is now fit and leading the Twenty20 side out in New Zealand. He just needs some overs under his belt outdoors, hopefully he will get that and hopefully he will be ready for the Twenty20 games, the one-dayers and the Test matches afterwards.
"He is a massive player for us, he has delivered in big games before. This is such a big summer and winter coming up, we need all our big players hopefully fit and available throughout the whole time."
Broad claimed a hat-trick during England's T20 victory over a New Zealand X1 earlier today.