i hope my answer help your question.
first,~~하기로 했어요 original is ~~ 하기로 하다.
~~ 하기로 하다 = [~~ 하다 + ~~ 기로] + ~~ 하다(do) ,
~~ 하 (다 lost.) +기로 = (plan someone)
* ~~기로 (a plan something, but only Verb)
하기로(plan do something)
읽기로(plan read something)
보기로(plan see some....)
마시기로(plan drink some.....)
and, 하기로 했어요 is a report who someone, like a 'mother, i decide some it. '
친구와 만나기로 했어요 ( i decide to meet my friend )
밥을 먹기로 했어요 ( i decide to eat meal )
여동생을 깨우기로 했어요 ( i decide to wake up my littlesister )
P.S. may i thing you have confused by 결심,
결심 also can use a Decide, but more same Determination.
/나는/ /결심했다/ /공 부/ /열심히 하기로/
/i/ /Determination/ /study/ /hard/