The two-match Test series later in the month will be the first time Cook has been skipper in England.
England captain Alastair Cook is looking forward to being captain of the Test side for the first time on home soil later in May, when the Three Lions host New Zealand.
Cook took the captaincy role on a full-time basis in 2012 after previous skipper Andrew Strauss stepped down from the position.
Since then the opener has led his country out in four Test matches in India over the winter, followed by a three-match series in New Zealand earlier this year.
The 28-year-old also filled in twice as leader when England played in Bangladesh, with regular captain Strauss not travelling on the tour.
Therefore the upcoming five-day matches at Lord’s and Headingley will be the first time Cook will have led his team out in his home nation and the Essex batsman is relishing the opportunity.
The first match against the Black Caps starts on 16 May at Lord’s.