The reviews of the two bodies, which give out grants totalling hundreds of millions of pounds a year, were announced in the government’s The Culture White Paper, published last week.
The paper sets out what the government says is the first strategy for arts and culture in more than 50 years and includes a new expectation from government that all publicly funded arts organisations must improve access for young people from disadvantaged backgrounds.
The paper, announced by Ed Vaizey, the culture minister, says "arts organisations that receive public money must show they are reaching out and increasing access for young people from disadvantaged backgrounds to help find the stars of tomorrow and open arts and culture up for all".
It says the Department for Culture, Media & Sport will carry out "tailored reviews" of ACE and the HLF, plus what the paper calls a "wide-ranging review of the museums sector".
The reviews of the two grant-making bodies will consider how they carry out their roles in supporting the cultural sectors, how they work together and with Historic England and VisitEngland, and how they work with local authorities and other partners.
The museums review will "consider big questions around the national infrastructure, including the roles of government, Arts Council England and the Heritage Lottery Fund in nurturing the sector".
All the reviews will be completed by summer 2017, the paper says.
The paper says the government will introduce the new Great Place Scheme, which will "bring national arts and heritage lottery funders together to make culture a core part of local authority plans and policies".
Carole Souter, chief executive of the Heritage Lottery Fund, wrote in a blog that there was a lot to be positive about in the white paper.
"Certainly, the white paper fully embraces heritage as an essential part of the government’s vision, and there is a firm recognition of the role it plays supporting jobs, skills and tourism and making our towns, cities and communities better places to live," she said.
A statement from Arts Council England welcomed the publication of the paper and said it was a vote of confidence in the arts and cultural sector.
But the paper highlighted challenges to funding, especially outside London, the statement said.