The former Florida governor will “actively explore the possibility of running for President”, he wrote on Facebook on Tuesday.
He will also create a political action committee to “facilitate conversations with citizens across America”.
Mr Bush has pro-immigration views, an issue likely to top the 2016 campaign.
But his views on this subject and on education have enraged some conservative Republicans.
Bush is not the only familiar name circling the upcoming election.
Former First Lady and US Secretary of State Hillary Clinton is currently the frontrunner for the 2016 Democratic ticket.
The announcement marks the first major Republican candidate to make a formal move toward announcing candidacy for the 2016 presidential nomination.
“In the coming months, I hope to visit with many of you and have a conversation about restoring the promise of America,” Mr Bush wrote on Facebook.
His committee, named Leadership PAC, will help “support leaders, ideas and policies that will expand opportunity and prosperity for all Americans”.
He is not expected to to announce his decision until next year “after gauging support”, Kristy Campbell, a spokeswoman for Mr Bush, told the Associated Press news agency.
“This is a natural next step and represents a new phase of his consideration process,” she added.
Mr Bush’s Facebook statement is the strongest yet to indicate he plans to attempt to become the third member of his family – after his father, George HW Bush, and brother – to become leader of the US.
During two terms as governor of Florida, he overhauled the state’s education system and pushed for substantial tax cuts.
In a recent televised interview, Mr Bush claimed he “would be a good president” and promised to release a cache of emails from his time as governor.
Other names in the frame for the Republican nomination include Senators Rand Paul, Marco Rubio and Ted Cruz, and Governor Chris Christie.