He will replace Sir Charles Montgomery, who will be moving on in September after a distinguished 44-year career in the Royal Navy and Civil Service.
Mr Lincoln, who is currently Director-General of the Home Offices Crime, Policing and Fire Group (CPFG), will take up his new role in the autumn.
He will take overall responsibility for Border Force, a law enforcement command within the Home Office which secures the UK border by carrying out immigration and customs controls for people and goods entering the UK.
Mr Lincoln joined the Home Office in 2014 as national security director and then acting Director-General in the Office of Security and Counter Terrorism (OSCT) before joining CPFG.
Permanent Secretary Philip Rutnam and Second Permanent Secretary Patsy Wilkinson said:
Paul has done a tremendous job in leading CPFG over the past year, overseeing and driving its mission to keep people safe, cut crime, protect the vulnerable and reform police, fire and rescue services.
We would like to thank Paul for his leadership in this area and look forward to working with him as director-general for Border Force.
We would also like to thank Sir Charles for his dedicated years of service in the Home Office and, before that, the Ministry of Defence. Sir Charles has played a vital role in leading Border Force through a period of significant transformation whilst ensuring that the UK borders remain secure.
Commenting on his appointment, Paul Lincoln said:
I am delighted to have the opportunity to lead Border Force at such an important time. I look forward to working with colleagues across the organisation who strive to secure our border and promote national prosperity.
It has been a privilege to have been the Director-General of CPFG, working with colleagues and partners to make the country a safer place.
Sir Charles was appointed Director-General of Border Force in 2013 after a long career in the Royal Navy.
Sir Charles Montgomery said:
It has been a great privilege for me to lead the men and women of Border Force in fulfilling its vital role and meeting its operational objectives.
I am committed to making this personal contribution until the very last moment I leave the office.
I am delighted that I am to be succeeded by Paul, who has all the personal and professional qualities to be an outstanding Director-General of Border Force.