"Der Aaye Durasta Aaye!! I welcome UK Govt's step for active engagement & strengthening relations with Guj. God is Great," Modi wrote on his Twitter account.
A decade after the Gujarat riots, in which three Britons were killed, Swire has asked his high commissioner in New Delhi to visit Gujarat and meet with Modi and other senior figures.
"This will allow us to discuss a wide range of issues of mutual interest and to explore opportunities for closer cooperation, in line with the British Government's stated objective of improving bilateral relations with India," Swire said in a statement.
British officials were banned from meeting with Modi after the Gujarat riots and the US has a travel ban on him.
Britain's turnaround disappointed human rights campaigners despite Swire giving an assurance he wants to secure justice for the families of British victims of the 2002 riots.
"We want to support human rights and good governance in the state," Swire said.
"This is a complete red herring. The British government is hiding behind the façade of human rights," said Indian-origin rights campaigner Amrit Wilson of the South Asia Solidarity Group.
"This is all about British companies wanting to do business in Gujarat."
Threats of widespread demonstrations by rights groups are often cited as the main reason for Modi calling off a planned visit to Britain in 2005.
In his statement, Swire said, "We also want to provide the best possible support for British nationals who live in, work in or visit Gujarat; and to the many Gujaratis who now make up one of the most successful and dynamic communities in the UK.
"I feel that active engagement will help further these interests. We will consider in the light of the High Commissioner's visit how best to take forward our relationship with Gujarat."
Der Aaye Durasta Aaye!! I welcome UK Govt's step for active engagement & strengthening relations with Guj. God is Great nm4.in/T7QvZ8— Narendra Modi (@narendramodi) October 11, 2012
Der Aaye Durasta Aaye!! I welcome UK Govt's step for active engagement & strengthening relations with Guj. God is Great nm4.in/T7QvZ8