McKinstry has been working in the west African country for the last two years for the Craig Bellamy Foundation, which runs an academy and a league for youth teams.
The Sierra Leone FA said McKinstry would take charge of the country's remaining Group B matches against Tunisia and the Cape Verde Islands in June and Equatorial Guinea in September.
McKinstry, who has had little experience at senior level and mainly been in charge of youth development programmes, takes over from the Swede Lars-Olaf Mattsson who resigned a fortnight ago after their World Cup defeat in Tunisia, citing frustration with the organisation around the team.
Sierra Leone have four points from three matches in the group, second behind Tunisia on nine points at the halfway stage of the campaign.
- Sports & Recreation