The Football Association of Ireland (FAI) have been in the process of trying to find a permanent successor to Stephen Kenny.
That led to national team legend O'Shea taking the reins on a temporary basis for friendly internationals against Belgium and Switzerland in March.
O'Shea made a positive impression in his first fixture, earning a goalless draw against a weakened Belgium outfit in Dublin.
However, the former Manchester United man would then oversee a 1-0 reverse to Switzerland, a Xherdan Shaqiri free kick proving to be the difference.
At the time, it was expected that a full-time head coach would be at the helm for the June encounters against Hungary and Portugal, two more nations that have qualified for Euro 2024.
Instead, the decision has been made to extend the stay of O'Shea, who has acknowledged in the past that he wants to remain in the role.
What does O'Shea have to say?
Speaking to the FAI's official website, O'Shea said: "I'm looking forward to continuing as interim head coach for two great games in June against Hungary and Portugal.
"Both matches represent great challenges but I was really happy with what I saw from the players in both matches in March and we'll be looking to build on some of those positives in June, but also, get that win which I thought the group deserved.
"I have been in contact with Marc Canham (director of football) since the March fixtures and last week, he asked me about stepping in again and as I said before, it is always an honour to represent your country so delighted to continue as interim head coach for June and the work will begin straight away.
"Also, great to confirm the coaching and performance team will remain for the June fixtures which is great for continuity with the players and staff."
UEFA Nations League to follow
Republic of Ireland will be using the next double-header as preparation for the upcoming UEFA Nations League campaign, which begins in September.
The Boys In Green have been placed in a group alongside England, Greece and Finland, their first fixture coming at home to the Three Lions on September 7.