He first found his own brother, Simon, and said to him, "We have found the Messiah!" (which is, being interpreted, Christ{"Messiah" (Hebrew) and "Christ" (Greek) both mean "Anointed One".}).
We have found the Messiah ... implies that Andrew, Peter, James and John had been earnestly expecting and waiting for the Messiah and that they had been searching to find him, their attitude of expectancy having resulted from John the Baptist's preaching, "Repent ye, for the kingdom of heaven is at hand"  (Matthew 3:2).  Thus, the prior attitude of those first disciples accounts for their rapid progress.  They first addressed the Lord as "Rabbi"; and, after only a day with him, they affirmed that he was the Messiah.  Note that John again interpreted the Jewish term "Messiah" for his Gentile readers.