The nomination is likely to reinforce market expectations the central bank will maintain its massive stimulus programme to reflate the economy and fire up inflation to its elusive 2% target.
Adachi, 54, an economist at Japan's Marusan Securities, would replace Yutaka Harada, a similarly minded board member whose term expires on March 25.
The nomination is unlikely to tip the balance of the board, which is split between those who see room for the BOJ to ramp up stimulus and others who are more worried about the rising cost of prolonged easing such as pressure on bank profits from years of ultra-low interest rates.
"He is among a group of reflationist-minded economists, so may call for additional monetary easing or dissent to keeping policy steady," said Nobuyasu Atago, chief economist at Okasan Securities. "But he's unlikely to affect the vote count of the current board."
The BOJ has recently voted 7-2 to keep its negative interest rate target steady, with Harada among the dissenters.
In an interview with Japan's Nikkei newspaper in 2017, Adachi said the BOJ should buy foreign bonds or accelerate the pace of its purchases of exchange-traded funds (ETF) to prop up inflation. He was against deepening negative interest rates.
Adachi is close to Koichi Hamada, an economic adviser to Prime Minister Shinzo Abe, and has supported BOJ Governor Haruhiko Kuroda's huge asset-buying programme deployed in 2013 to shock Japan out of deflation.
Years of heavy money printing have failed to spur inflation, however, and some of the reflationist-minded economists have shifted their attention towards the role fiscal spending could play in reflating the economy.
In comments that could cause controversy, Adachi said in a tabloid column in 2016 that the voting pattern of supporters for U.S. President Donald Trump was similar to one that brought the Nazis to power in Germany. He was alluding to how deep strains in the economy had made the German people disgruntled to take a "high-risk, high-return" option in polls.
Under a policy dubbed yield curve control (YCC), the BOJ guides short-term rates at -0.1% and the 10-year government bond yield around 0%. It also buys government bonds and risky assets such as ETFs as part of efforts to funnel money to the economy.
It does not buy foreign bonds on the view doing so would infringe upon the Ministry of Finance's jurisdiction on currency policy.
The government's pick of Adachi needs to be approved by both houses of the parliament, which should proceed smoothly as Prime Minister Shinzo Abe's ruling bloc holds a solid majority in both chambers.
With global risks weighing on Japan's economy and inflation well below its target, many market players expect the BOJ to keep monetary policy steady for the foreseeable future to help underpin a fragile recovery.
(Reporting by Tetsushi Kajimoto and Yoshifumi Takemoto; Additional reporting by Kaori Kaneko and William Mallard; Editing by Richard Pullin, Christopher Cushing & Kim Coghill)
By Tetsushi Kajimoto and Yoshifumi Takemoto