Teams from the Nicolson Institute in Stornoway, Lewis, reached five finals in the North of Scotland Cup and won four of them.
The senior girls category of the competition was won by the secondary school for the sixth year running.
Strachan has visited the school to meet the pupils and their teachers.
The tournament is open to all secondary schools in the north of Scotland, which includes the Highlands and Northern Isles.
Teams from the Nicolson Institute won the senior and junior girls trophies and also the senior and under 14 boys finals.
The under 13 boys were also in the final of their age group.
Catriona Stewart, chairwoman of education and children's services at the islands' local authority Comhairle nan Eilean Siar, said: "Despite living on an island, our pupils have proven that they can be successful at national level through sheer diligence and determination despite not having access to as many facilities as mainland youngsters may have.
"The Nicolson Institute football teams have done themselves proud for a number of years now, but this year has been a particularly remarkable year."
The councillor added: "It is testament to the hard work of all the pupils, coaches and parents who support them that the Scotland national team manager felt it appropriate to come and congratulate them here today.
"Who knows - maybe we will see some of our youngsters play for the national team in years to come."
Scotland national team manager Gordon Strachan has congratulated island pupils following their success in a Scottish schools football competition.