Home Secretary Theresa May said Mr Bristow would lead an agency of "powerful operational crime fighters".
The NCA becomes fully operational in 2013 when it takes over from the Serious Organised Crime Agency.
Its expanded role will include powers to order police forces to run operations into drugs and trafficking.
As well as replacing the Serious Organised Crime Agency (Soca), the new agency will take in the work of the Child Exploitation and Online Protection Centre (Ceop), and also house the national cyber crime unit. It will also cover border policing and economic crime.
"For too long we have lacked a strong, collaborative national response in the fight for criminal justice. The NCA will make the UK a more hostile environment for serious and organised crime and strengthen our border," Mrs May said.
She said Mr Bristow would play "a vital role" in developing the agency.
Details of an extensive policing shake-up, which included the creation of the National Crime Agency, were unveiled last year by Mrs May in a Home Office consultation paper - Policing in the 21st Century.
She described it as the "most radical reform of policing for 50 years".
Mr Bristow said he would work with the government and other crime agencies "to ensure that the NCA delivers the maximum protection possible for communities within the resources it has available".
"In partnership with other law enforcement agencies, we will ensure that criminals are identified, pursued and brought to justice, their groups dismantled and their activities disrupted. We will do even more to strip away their illegally obtained assets," he said.
Association of Chief Police Officers president Sir Hugh Orde said Mr Bristow had been chosen from "a very strong field of police leaders" to lead the NCA.
"A better co-ordinated response between the international reach and capability of this new agency and the 'eyes and ears' of local neighbourhood policing teams can help keep our streets and communities safer," Sir Hugh said.
Mr Bristow was appointed chief constable of Warwickshire Police in 2006 and chairs the G8 Law Enforcement Group.
He has been the Association of Chief Police Officers' head of crime and worked in the West Midlands Police and as director of the National Criminal Intelligence Service.

The Merthyr and Rhymney AM will stand down before this year's election after 17 years in Cardiff Bay.
Speaking to BBC Radio Wales' Sunday Supplement programme, he said many politicians, including some in his own party, were nervous and sceptical about devolution in 1999.
But that view is now "long gone".
While he was "a very early convert", he said the closeness of the referendum result - 50.3% voted for and 49.7% voted against setting up the assembly - created "a great deal of nervousness".
He said: "My opinion was always the proof of the pudding is in the eating, it's about what the institution does - in terms of social change - that really matters."
Mr Lewis felt strongly that devolution could be used to tackle areas in which Wales was at a particular disadvantage to England, including health, education and combating poverty.
The former chemistry teacher described taking on the education portfolio as "a dream come true" and said reforms to the curriculum and teacher training were two of his proudest achievements.
He said: "The old England and Wales schools-based education agenda no longer exists.
"Wales now has its own distinctive path and own distinctive future in terms of what our schools are going to look like."
He said the reforms happening here were based on "real evidence" and not "ideologically driven", which is what he fears is happening in England with the "marketisation of education".
By implementing a Scandinavian-style model - that includes children learning through play -  he hopes teachers will be better skilled and standards will rise.
"We're not emulating England, we're emulating the best," Mr Lewis said.
This is despite an assumption he believes is made by many that Wales should see England as a "gold standard" and if something different is tried here, it is somehow suspect and second rate.
"I hope, that as devolution has matured over the years, we are finally beginning to break away from that kind of mentality," he added.
"We are quite capable of setting out our own agenda and following it and basing it, in global terms, on what the best looks like.
"That's the real dividend from devolution. That should always be where we're thinking.''
The first head of the UK's incoming National Crime Agency (NCA) will be Keith Bristow, currently chief constable of Warwickshire.
[NEXT_CONCEPT]
Wales has "broken away" from England and is now capable of setting its own agenda thanks to devolution, outgoing education minister Huw Lewis has said.