Eisenkot, currently deputy chief of staff, will replace Lieutenant General Benny Gantz, whose four-year term ends in February 2015.
The appointment is subject to government approval.
Defence Minister Moshe Yaalon called Eisenkot the best choice to face Israel's "complex security challenges".
Replacing him as new deputy chief of staff will be Major General Yair Golan, currently head of the northern command, Yaalon added.
Prime Minister Benjamin Netanyahu said Eisenkot was "selected from an excellent group of generals" and wished him luck.
Signup to our newsletter and follow us on Facebook and Twitter!
The 54-year-old began his military service as an infantryman in the Golani Brigade, rising through the ranks to command it.
He was military secretary to premier and defence minister Ehud Barak between 2009 and 2011, during which Israeli media reported he was involved in negotiations with Syria.
Eisenkot was later appointed commander of the Judea and Samaria division, Israel's term for the West Bank, before becoming head of the operations directorate and eventually northern command chief from 2006 to 2011.
It was during his northern command tenure that he wrote Netanyahu a "personal letter" discouraging an attack thwart Iran's nuclear programme, which Israel fears has a military objective.
According to Haaretz newspaper, Eisenkot warned that such an attack would cause a long war with Iran and its Lebanese-based Hezbollah militia, while also souring relations with the United States.
Haaretz noted that contrary to when Eisenkot wrote the letter, "an Israeli attack on Iran is currently not on the agenda", but it could become relevant again in July 2015, the new deadline for nuclear negotiations between Iran and world powers.