Nielsen, 38, is head coach at the Centre of Excellence in Brisbane, which includes managing the respected Australian Institute of Sport (AIS) men's cricket programme.
He took over that role in 2005 after spending three years assisting Buchanan in the coaching of the Australian team.
Nielsen, a former wicketkeeper-batsman for South Australia, will begin work in his new role after the World Cup, Cricket Australia said on Monday.
Nielsen was appointed a week after former Australian Test player Tom Moody, the highly regarded coach of Sri Lanka, announced he was not interested in the position.
"I'm incredibly proud, honoured and excited to have been offered this opportunity," Nielsen said in a statement.
"Moving forward, this job represents a great opportunity to work with a fine group of players who are an excellent cricket team.
"Over the coming period there will be some transition in the playing group and I look forward to working with the exciting emerging talent in this country as well as the established members of the squad.
"Filling John Buchanan's shoes will be a big job. John is a leading light in cricket coaching globally and his record speaks for itself.
"I've been privileged to be a member of his support staff and the benefits I'll inherit in terms of the structure around the playing group have largely come around due to John's hard work.
"John will continue to be a regular sounding board for me in the role."
Cricket Australia chief executive James Sutherland said the fact that an appointment had been made from within the coaching system reflected the quality of the game's high performance programmes.
"His relationships with our established players and rising stars are excellent and I know the playing group is looking forward to working with him when John Buchanan retires after the World Cup," Sutherland said.
Buchanan endorsed Nielsen's appointment, saying his former assistant had a huge desire for the Australian team to continue to move forward.
"Tim has demonstrated throughout his time in the state system, as assistant coach to the national team and head coach in the institute programme, his dedication, desire and enthusiasm for the game.
"He also has a huge desire for the team to keep improving. Each system he's been involved with has prospered. He is an ideal man, together with the Australian captain, to take the Australian team into the future."
Australian captain Ricky Ponting said it was important that the new coach had a deep understanding of the players.
"Tim was an outstanding assistant coach with the national team and has led a very successful programme at the Centre of Excellence," Ponting said.
"One of the most important things to have as a coach is a deep understanding of any individual player and their techniques.
"Tim has worked with most of the young talent in the country at the Centre of Excellence and is well placed to guide that young talent.
"On a personal level I'm delighted, having played against Tim and having worked with him when he was assistant coach. We have an excellent working relationship and I'm looking forward to the challenges that lie ahead."