https://www.presidency.ucsb.edu/documents/executive-order-10973-administration-foreign-assistance-and-related-functions
As you can see by Section 1 alone... Congress gave the Executive the authority via multiple legislation
PART V. FUNDS
SEC. 501. Allocation of funds. Funds appropriated or otherwise made available to the President for carrying out the Act shall be deemed to be allocated without any further action of the President, as follows:
(a) There are allocated to the Secretary of State all funds made available for carrying out the Act except those made available for carrying out Part II of the Act.
(b) There are allocated to the Secretary of Defense funds made available for carrying out Part II of the Act.
SEC. 502. Reallocation of funds. The Secretary of State and the Secretary of Defense may allocate or transfer as appropriate any funds received under subsections (a) and (b), respectively, of section 501 of this order, to any agency, or part thereof, for obligation or expenditure hereby consistent with applicable law.
Congress gave the President the legislation to create USAID which gives the Secretary of State (through the President) the appropriation of funds.