Parliament approved on Saturday the new 18-article constitution, which would create an executive presidency.
Erdogan's signature would be the final executive step in the adoption of the bill ahead of the public vote, a date for which Prime Minister Binali Yildirim said would be announced this week.
Parliament approved on Saturday the new 18-article constitution, which would create an executive presidency for the first time in Turkey, in the final of two readings.
Brawls erupted in parliament during debates over the bill, which critics fear will lead to one-man rule.
The changes are the most far-reaching constitutional shift since the creation of modern Turkey in 1923.
Erdogan told journalists in Madagascar during a tour of east Africa that he would make his decision on the bill "without delaying too much because the people are waiting for this".
The referendum would be held 60 days after Erdogan's formal approval is published in the Official Gazette, Yildirim said, adding that the date for the plebiscite was expected to be announced this week by the Supreme Election Council (YSK).
"I think it will be in the first half of April, a suitable date would be up until the 20th (of April)," he said.
The new constitution would give the head of state the power to appoint and dismiss ministers. There would be no longer a prime minister but instead one or more vice presidents.
Turkish officials have dismissed concerns over the legislation, saying the changes are needed to bring in effective government in a system similar to the United States or France.
But the main opposition Republican People's Party (CHP) said it would challenge the bill in the constitutional court, an action which Erdogan dismissed as an irrelevance.
"We don't have the right for any preventative action (or) to say 'why are you going there?' in this regard," he said.
"I hope that the constitutional court will at once give its decision on this issue as well."
The ruling Justice and Development Party (AKP) has only 317 seats in the 550-seat parliament and sought the support of the far-right Nationalist Movement Party (MHP) to pass the bill in two readings earlier this month.
But Yildirim insisted there would be no "joint campaign" with the MHP to get a "Yes" vote for the changes.
He defended the bill, saying MPs' powers would be "strengthened" and that they would still have the right to bring draft laws to parliament.
Transport Minister Ahmet Arslan also said a presidential system would speed up the decision-making process for infrastructure projects in an interview with the state-run Anadolu news agency on Wednesday.
While Yildirim was speaking the lira plunged to 3.82 against the US dollar, a loss of over one percent on the day, amid fears of continued political instability.