PM Modi welcomed King Abdullah with a warm hug as he alighted from the aircraft.
In a tweet, External Affairs Ministry spokesperson Raveesh Kumar said that PM Modi, deviating from protocol, "welcomes His Majesty at the airport".
"India attaches great importance to its ties with Jordan," Mr Kumar said.
This is King Abdullah's second visit to India after his visit along with Queen Rania in 2006.
King Abdullah will hold talks with PM Modi on Thursday during the course of which the two sides will discuss the entire gamut of bilateral relations as well as regional and international issues of mutual interest.
President Ram Nath Kovind will host a banquet in honour of King Abdullah while Vice President M. Venkaiah Naidu and External Affairs Minister Sushma Swaraj will call on the visiting dignitary.
During the day, the King will also participate in a CEO Round-table followed by India-Jordan Business Forum jointly organised by Industry bodies Ficci, CII and Assocham.
India-Jordan trade stood at $1.35 billion in 2016-17, according to figures provided by the External Affairs Ministry.
On Thursday, the King will deliver a special address on "Promoting Understanding and Moderation", organised by the India Islamic Centre at Vigyan Bhawan.
Earlier this month, King Abdullah hosted PM Modi at his residence in Amman. Jordan had facilitated PM Modi's transit to Palestine in what was the first ever prime ministerial visit from India to that West Asian nation.