Mr Brokenshire, who served as Northern Ireland secretary and security minister, had been suffering from lung cancer and died on Thursday evening.
MPs across the county have paid tribute to the 53-year-old, who was the Conservative MP for Old Bexley and Sidcup, on Twitter.
Wrekin MP Mark Pritchard said: "My thoughts and prayers are with his family at this very difficult time. A courteous, polite and dedicated public servant - abd politician. A diligent and first class Minister - especially Security Minister. RIP."
North Shropshire MP Owen Paterson said: "I’m so sorry to hear of the death of my colleague James Brokenshire who has died far too young.
"A former Northern Ireland Secretary who was widely liked and respected across the political divide."
Shrewsbury MP Daniel Kawczynski called him an "outstanding" MP and said he would be missed by all colleagues.
Ludlow MP Philip Dunne said he had been "very sad to learn this tragic news".
"James was an utterly dedicated, genuinely gifted, lovely man who devoted himself to public service for all the right reasons," he added.
"Our public life is diminished by his untimely death."
Mr Brokenshire first announced he had been diagnosed with lung cancer in 2018.
He became vocal over calls for a national screening programme for lung cancer, and in April 2018 used a debate in Parliament to call for a national programme to improve poor survival rates.
He said much stigma surrounds lung cancer, with many people incorrectly believing it is only caused by smoking.
Thousands of pounds have been raised so far in his memory after his family set up a fundraising page to encourage people to share memories, photographs and donate.
Less than 24 hours after the page was announced on Friday, more than £12,000 had been pledged by the public to the Roy Castle Lung Cancer Foundation.