While the new policing boss said "proud and privileged" to be taking up the position, he acknowledged that there was a challenge to balance the workforce of the PSNI.
Before leaving the position former Chief Constable Sir George said that action must be taken to halt the falling number of Catholics joining the PSNI.
Mr Byrne said he had a number of aims in his new role.
"I'd like to say how proud and privileged I am to have been asked by the Policing Board to lead this great organisation as it continues its work to police Northern Ireland around the clock and keep you safe," the new Chief Constable said.
"My initial priorities are to get out and about across the country to hear first hand what makes the organisation tick and to see as many of our communities as possible
"Then it is to build on the work of those who have gone before me, to keep bringing down crime, see how we need to respond to new and changing types of crime as well as contributing more to the criminal justice system to make it more effective and to speed up justice for victims."
He acknowledged that there was a need to make the PSNI more representative.
"Looking ahead there is more work to do to improve how representative the organisation is of the communities we serve," Mr Byrne said.
"I want to revist our plans and ideas to make sure that the organisation reflects our communities as best as it can.
"But for now, it's about getting out from behind my desk and finding out how the PSNI ticks."
The SDLP has called for a return of 50:50 recruitment to boost the number of Catholics joining the PSNI.
When the PSNI replaced the RUC in November 2001 a policy of 50-50 recruitment of both Catholics and Protestants was introduced in an attempt to boost the number of Catholics in the force.
At the time the policy was introduced Catholics made up around 8% of the police force. The policy was discontinued in 2011.