Abu Khattab Qatadah (May Allah be pleased with him) reported: I asked Anas: "Did the Companions of Messenger of Allah (PBUH) use to shake hands?" He said: "Yes."[Al-Bukhari].
To shake hands with somebody is a welcome sign and the practice of the Messenger of Allah (PBUH). The social behaviour of the Companions also included handshaking along with saying `As-Salamu `Alaikum.'