Johnson has appointed Priti Patel as Home Secretary, Alok Sharma as International Development Secretary and Rishi Sunak as Chief Secretary to the Treasury.
The Cabinet also includes Pakistani-origin Sajid Javid in the top job of Chancellor.
"The 'desi' cabinet is a testament to just how diverse the UK is, and also what an impact the Indian diaspora makes in the UK. It is fantastic profile of the current state of UK," Asquith said at a media briefing.
To a question on Britain's new immigration policy under the new government, which is to leave the European Union by October 31, he said that Johnson has made it clear that the UK should "attract the best of brains".
Asquith said that Johnson "has made clear that he is a profound supporter of making sure Britain attracts the best of brains", and his government will "overlook the whole immigration process".
He added that Priti Patel "has made clear that once we leave the EU, we will not favour geographical barriers and it will be open to all, on the basis of merit".
Johnson has announced to explore an "Australian style points-based system" as part of "a radical rewriting" of the immigration system.
Both Johnson and Patel support "economic" migration and don't support giving priority to EU migrants - which could be beneficial for skilled Ind, including students who go to the UK to study.
The Prime Minister has instructed the Migration Advisory Committee, a panel of academics and economists who advise the government on migration policy, to re-design the UK's post-Brexit immigration system.
Patel has also announced that priority would be given to "those with the highest skills and the greatest talents - to attract those who add the most to our economy".
( With inputs from IANS )