Kernighan, who is also director of public policy, will leave the NCVO in June after 14 years with the umbrella body, before joining the NUS in July.
The NCVO, which is going through an organisational restructure, said it would begin recruiting for a new director of public policy soon. A spokesman said the role would be offered internally in the first instance.
But it will not be looking for a replacement for the deputy chief executive’s role, which will be divided between the remaining directors, the spokesman said.
Kernighan said: "I am delighted and excited to be appointed. The NUS has a very important role to play in helping the everyday lives of students, supporting students’ unions and helping to shape further and higher education in the UK."
Kernighan joined the NCVO as business development manager in 1998 from the Terrence Higgins Trust.
He replaces Matt Hyde at the NUS, who will leave next month to join the Scout Association as chief executive.
Sir Stuart Etherington, chief executive of the NCVO, said: "Ben has made a genuine difference to our whole sector. Behind the scenes his advocacy has had a significant influence on a wide range of government policy. In public, he has been a powerful campaigner on issues from charity tax to the Work Programme.
"Ben’s intelligence, communication skills and deep commitment to voluntary action have made a pivotal contribution to the development of the NCVO as the authoritative voice of the sector.
"The NUS is most fortunate to have gained such an outstanding strategic thinker. He leaves the NCVO with our warmest wishes for his new role."
Liam Burns, president of the NUS, said: "I believe that he is joining the organisation at an exciting time and that he is the right person to take the organisation forward. Under the leadership of Matt Hyde, the organisation has gone from strength to strength, and I am confident that Ben has the skills, experience and drive to see the organisation meet head-on its future strategic challenges."