The 29-year-old was one of four candidates on a shortlist for the job.
McKinstry previously led Sierra Leone into the top 50 of the Fifa world rankings as the youngest manager in international football.
His new appointment, as the successor to Englishman Stephen Constantine, will see him also take charge of the Under-23 and Under-20 teams.
He will now lead Rwanda in their qualification games for the 2017 Africa Cup of Nations, the 2018 World Cup and the 2016 Olympics.
The other coaches in the running for the job were former Chelsea assistant Jose Morais, Turk Engin Frat and German Hans Michael Weiss.
Constantine quit the post in January to take over as manager of the India national side.
McKinstry was appointed by the Leone Stars at the age of 27 and lost only one of his first six matches.
But following defeats by Ivory Coast and DR Congo in the 2015 Africa Cup of Nations qualifiers, he was sacked - only six months after he had been given the job on a permanent basis.
Northern Irishman Johnny McKinstry has been named as the new coach of the Rwanda national football team.