You're the person I was hoping to meet.
sei la per-SO-na ke spe-RA-vo di in-con-TRA-re — stress on 'so-', 'ra-', 'tra-'. 'Speravo' uses the imperfect — spe-RA-vo.
A sincere and brave declaration — saying you had hoped for someone like this implies you were open, ready, and that this person is the realisation of that hope.
'Sei la persona che' = you are the person that. 'Speravo di incontrare' = I was hoping to meet (imperfect of 'sperare' + infinitive 'incontrare'). The imperfect 'speravo' suggests the hope was ongoing — a sustained longing now fulfilled.
Eri quello/a che mancava.
You were what was missing.
'Mancava' — imperfect of 'mancare' — something was absent and now you have it
Non sapevo cosa cercassi finché non ti ho incontrato/a.
I didn't know what I was looking for until I met you.
Beautiful — desire that was shapeless until given a face
Speravo in qualcuno come te.
I was hoping for someone like you.
Slightly softer version — hopes for someone similar, not the exact person
Italian romantic culture has a long tradition of 'l'attesa' — the wait. The idea that you were waiting for someone without knowing it is deeply embedded in Italian love poetry and song. Saying 'speravo senza saperlo' (hoping without knowing) is genuinely poetic and culturally resonant.