Laidlaw, who played sevens for Scotland between 2004-07 and was also assistant coach at Super Rugby side Wellington Hurricanes, returns for another stint in sevens after previously being New Zealand's skills coach and video analyst.
Laidlaw will take up the role next June and will be charged with guiding New Zealand to a men's gold medal at the 2020 Tokyo Games after they missed out in Rio under long-serving coach Tietjens.
"We are very excited to have selected a coach of Clark's calibre to lead the All Blacks sevens to success at the Tokyo Olympics in 2020," NZR General Manager of Rugby Neil Sorensen said in a media release.
"Our priority was getting the right coach with the long-term vision to win Olympic gold. So while we would have loved Clark to start straight away, we are happy to wait until next year because he is the best person for the job to build a winning sevens team over the long term."
Former All Blacks sevens players Scott Waldrom and Tomasi Cama will form an interim coaching team for upcoming world series tournaments starting in Dubai next month.
Fiji won the inaugural men's sevens Olympic title at the Rio Games in August.
(Reporting by Ian Ransom in Melbourne; Editing by Greg Stutchbury)
