Universal Media Studios and ITV's Hollywood division, ITV Studios Inc, will initially co-produce a two-hour pilot for NBC.
The agreement includes three pilot commitments over the next two years.
Dame Helen Mirren's character, detective chief inspector Jane Tennison, will be played by an as yet uncast US actress.
The show will be adapted by 'Without a Trace' creator Hank Steinberg.
Angela Bromstad, NBC and Universal Media Studios president of primetime entertainment, said: "We want to carefully choose a couple of iconic titles this year to reinvent, and our intention is to create another classic television show from this brilliant original format.
"Hank Steinberg was key in helping us secure this project, and we are incredibly excited about his modern vision for the show."
Previously, ITV has sold mostly reality TV programmes to US networks, including 'Hell's Kitchen', 'I'm a Celebrity, Get Me Out of Here' and 'Celebrity Fit Club'.
These shows are among a string of programmes sold by UK broadcasters to their US counterparts.
BBC Two's ' The Office', starring Ricky Gervais, has undergone a successful remake in the US on NBC. The sixth season of the adaptation is set to premiere in the US later this month.
Another BBC comedy, 'Steptoe and Son', was bought by NBC and remade into a US version called 'Sanford and Son'. It aired for six seasons in the 1970s.
Three attempted remakes of 'Fawlty Towers', also a classic 70s comedy, were created for the US market. Two were produced by the ABC -- 'Chateau Snavely' and 'Amanda's' - and a third, called 'Payne', was made by CBS. All three remakes failed to appeal to US viewers.
A US version of the BBC's time-travel police show 'Life on Mars' was also produced and broadcast on the ABC but was not well received.