Answer by taking a quote from the following article:

Sayyid Ruhollah Musavi Khomeini (Persian: syd rwHllh mwswy khmyny [ru:hol'la:he khomei'ni:] ( listen); 24 September 1902 - 3 June 1989), known in the Western world as Ayatollah Khomeini, was an Iranian Shia Muslim religious leader and politician. He was the founder of Iran as an Islamic republic and the leader of its 1979 Iranian Revolution that saw the overthrow of 2500 years of Persian monarchy and Mohammad Reza Pahlavi, the last Shah of Iran.

Khomeini was not allowed to return to Iran during the Shah's reign (as he had been in exile). On 17 January 1979, the Shah left the country (ostensibly "on vacation"), never to return. Two weeks later, on Thursday, 1 February 1979, Khomeini returned in triumph to Iran, welcomed by a joyous crowd estimated (by BBC) to be of up to five million people. On his chartered Air France flight back to Tehran 120 journalists accompanied him, including three women. One of the journalists, Peter Jennings, asked: "Ayatollah, would you be so kind as to tell us how you feel about being back in Iran?" Khomeini answered via his aide Sadegh Ghotbzadeh: "Hichi" (Nothing). This statement--much discussed at the time and since--was considered by some reflective of his mystical beliefs and non-attachment to ego. Others considered it a warning to Iranians who hoped he would be a "mainstream nationalist leader" that they were in for disappointment.  To others, it was a reflection of an unfeeling leader incapable or unconcerned with understanding the thoughts, beliefs, or the needs of the Iranian populace.  Khomeini adamantly opposed the provisional government of Shapour Bakhtiar, promising "I shall kick their teeth in. I appoint the government." On 11 February (Bahman 22), Khomeini appointed his own competing interim prime minister, Mehdi Bazargan, demanding, "since I have appointed him, he must be obeyed." It was "God's government," he warned, disobedience against him or Bazargan was considered a "revolt against God."  As Khomeini's movement gained momentum, soldiers began to defect to his side and Khomeini declared ill fortune on troops who did not surrender. On 11 February, as revolt spread and armories were taken over, the military declared neutrality and the Bakhtiar regime collapsed. On 30 and 31 March 1979, a referendum to replace the monarchy with an Islamic Republic passed with 98% voting in favour of the replacement, with the question: "should the monarchy be abolished in favour of an Islamic Government?"

Why did he return to Iran?
Thursday, 1 February 1979, Khomeini returned in triumph to Iran, welcomed by a joyous crowd estimated (by BBC) to