"This is what I was looking for!" he shouted.

Literal

"This [subject-が] searching-was thing [copula-だ]" [quotative-と] he [topic-は] shouted.

探していた is ~ていた form marking past ongoing action ('was searching'). The whole phrase 探していたもの is a relative clause modifying the final もの ('the thing [I] was searching for') — note that the が-marked subject inside the relative is omitted. The matrix verb 叫ぶ ('to shout') is more emotionally charged than 言う.