The government accepted recommendations by the Senior Salaries Review Body, saying pay restraint was one of the "difficult choices" it faced.
The award comes amid a row over the 1% cap on public sector rises.
After the general election, some ministers suggested a rethink, putting pressure on Chancellor Philip Hammond.
The government says its policy has not changed, and last week teachers were told they faced another year of 1% rises.
Most public sector pay is set by ministers after receiving recommendations from different pay review bodies.
These bodies have to take into account government policy, which since 2013 has been for a 1% increase across the public sector, although in theory they are able to recommend higher increases.
The Senior Salaries Review Board covers the senior civil service, senior military officers, the judiciary and senior managers working for arm's length bodies of the Department of Health.
For each group, the board recommended a 1% rise, which has been accepted by ministers.
In a written statement, Cabinet Office Minister Damian Green said the government "greatly values" public servants' work and understands the need to recruit, retain and motivate staff.
He added: "However, there is a trade-off between pay and jobs in many public services, and pay restraint is one of the many difficult choices the government has had to make to help put the UK's public finances back on track.
"Senior public sector workers, like everyone else, will have to continue to play their part to ensure we deliver job security for working people across the country."
Naomi Cooke, of senior civil servants' union the FDA, welcomed a government promise of a review of senior salaries, but added: "What should be abundantly clear is that this cannot be achieved within a 1% straitjacket.
"Reform of senior civil service pay needs to be fully funded and it needs to happen soon - the current government pay policy is failing and is doing so in a way that costs civil servants and costs the public dear."
Senior civil servants, military officers and judges are to receive 1% pay rises this year, ministers have announced.