Theresa May will now have to replace the 50-year old MP, who has been doing the Northern Ireland job since July 2016.
The switch, part of a long-awaited Cabinet reshuffle by May, comes almost a year to the day since the collapse of the once-troubled province's semi-autonomous government.
Stormont, the regional parliament based in Belfast, has lain dormant for a year following the resignation of the late former Deputy First Minister of Northern Ireland Martin McGuinness, which prompted an inconclusive local election and a series of collapsed power-sharing talks.
It is being reported that Mr Brokenshire has "a small lesion on his right lung and will be having major surgery in the coming weeks".
"Clearly, my long term health and my family are my priorities and I intend to proceed with surgery at the earliest opportunity".
If Northern Ireland's politicians think her lack of experience means Ms Bradley will be a soft touch, however, they might consider how she has confounded low expectations in the past. I feel intently the impact on public services of the continuing absence of devolved government.
Sinn Fein argues that the deal gives the DUP unfair influence over British government policy in Northern Ireland, including over Brexit negotiations that will have major implications for Ireland's economy.
"Rather than looking for reasons not to restore the Executive, the parties should focus on why this matters now more than ever", he added.
Despite studious efforts by Brokenshire to be seen as an honest broker, some of the parties said a deal by the DUP previous year to prop up May's government made this impossible.