If you were to go all the way back to the US Constitution, authority over the budget has traditionally been held by the legislative branch. However, if you look across the larger course of United States history, what you will observe (particularly in the twentieth century) is that, as the scale of the Federal Government has increased, the power wielded by the executive branch (led by the President) has increased as well. Consider that the US government is far more bureaucratic and centralized today than it was two hundred years ago.
This is actually an important factor to be aware of when discussing 1974's Congressional Budget and Impoundment Control Act, since it was actually intended to counteract this kind of increase in executive power and reclaim for the legislative branch its traditional control over the budget. A key moment in this history can be found in 1921's Budget and Accounting Act, which, to quote the Congressional Budget Office itself (see reference link):
gave the President overall responsibility for budget planning by requiring him to submit an annual, comprehensive budget proposal to the Congress; that act also expanded the President's control over budgetary information by establishing the Bureau of the Budget (renamed the Office of Management and Budget in 1971).
Thus, if you look at this period of US political history, you will observe the executive branch encroaching upon the traditional responsibilities and powers of the legislative branch in these matters.
The Budget Act thus aimed to restore Congressional oversight and control of the budgetary process, shaped by Congress's conflict with the Nixon Administration. It established new congressional committees in the Senate and the House with oversight over the budgetary process, while also creating the Congressional Budget Office to inform Congress on these matters. Thus, this piece of legislation played a key role in restoring much of Congress's traditional authority over the US budget.
(Reference Note: in preparing this answer, I have relied heavily on the information provided by the Congressional Budget Office. The link to this website has been provided for reference purposes.)