Eisgruber, who graduated from magna cum laude from Princeton with a degree in physics in 1983, will succeed President Shirley Tilghman, The Daily Princetonian reported.
Tilghman announced in September that she planned to step down from her position after serving as Princeton's president for 12 years.
June will mark Eisgruber's ninth year as the university's provost.
In a November, Eisgruber told The Daily Princetonian that he he did not consider himself a candidate for the presidency.
"It is flattering that people would mention my name in this connection, but I do not consider myself a candidate," he said. "I have always assumed that I would return to my teaching and research -- which I love -- after my time as provost is done. That remains my [happy] expectation."