The 23-year-old Haryanto will make his race debut in Australia when the season starts on March 20.
"Melbourne will be a huge moment for me, my country, supporters and fans and I want to thank everyone who's been with me since I started in single seaters; 2016 is my chance to reward that faith and represent Asia in F1," Haryanto said.
His signing as team mate to German rookie Pascal Wehrlein completes the grid for the 2016 season.
Haryanto, who finished fourth in the GP2 feeder series last season with three race wins, will be the third Southeast Asian driver to compete in Formula One since the championship started in 1950.
The other two were Malaysian Alex Yoong, with Minardi in 2001-2002, and Thailand's Prince Bira (Birabongse Bhanudej) in the 1950s.
Haryanto was already the first Indonesian to drive a Formula One car, having tested with Manor's predecessors Virgin Racing in 2010.
The Indonesian's arrival in Formula One spells disappointment for Britain's Will Stevens, American Alexander Rossi and Spaniard Roberto Merhi, who all raced for Manor last season when the team was known as Marussia.
"Rio's huge following in Indonesia is great for the team and for F1. They are keen to see him on the grid and we're confident that we'll see him enjoying some exciting battles in the year ahead," Manor owner Stephen Fitzpatrick said.
Manor failed to score a point in 2015 but have rung the changes since then, with new management and drivers as well as Mercedes engines in place of ageing Ferrari ones.
Haryanto's place in the team had depended on raising funds in Indonesia, with Manor seeking 15 million euros ($16.71 million) according to local media.
The driver has been backed by state-owned Indonesian oil and gas company Pertamina but it was not immediately known how much they had contributed towards securing the drive.
($1 = 0.8979 euros)
(Reporting by Alan Baldwin; Editing by John O'Brien)
