There are several federal jurisdiction reports on this website, that accurately define the process of the requirement that the federal government must formally record the acceptance of a cession of jurisdiction from a state.   In 1940 the federal statute 40 USC 255 passed defining this requirement.  In 2002 the federal statute was updated and is now recorded in 40 USC 3112 , the requirement remains the same.

The Federal Legislative Jurisdiction Report Prepared for Public Land Law Review Commission, Land, and Natural Resources Division, United States Department of Justice, Washington, DC, May 1969 ( 1969 Federal Jurisdiction Report ) was commissioned by a US Congressman from Palisade, CO named Wayne Aspinall.   The 216 page Federal Legislative Jurisdiction Report and the US Codes are linked above.   The 1969 Federal Legislative Jurisdiction Report states on page 49, Paragraph 3, titled: Federal Statute Curtailing Federal jurisdictionIn 1940 the flood of transfers of legislative jurisdiction to the United States was stayed, by an amendment to section 355 of the Revised Statutes of the United States which eliminated the presumption of Federal acceptance. The amendment provided:  Notwithstanding any other provision of law, the obtaining of exclusive jurisdiction in the United States over lands or interests therein which have been or shall hereafter be acquired by it shall not be required; but the head or other authorized officer of any department or independent establishment or agency of the Government may, in such cases and at such times as he may deem desirable, accept or secure from the State in which any lands or interests therein under his immediate jurisdiction, custody, or control are situated, consent to or cession of such jurisdiction, exclusive or partial, not theretofore obtained, over any such lands or interests as he may deem desirable and indicate acceptance of such jurisdiction on behalf of the United States by filing a notice of such acceptance with the Governor of such State or in such other manner as may be prescribed by the laws of the State where such lands are situated. Unless and until the United States has accepted jurisdiction over lands hereafter to be acquired, as aforesaid, it shall be conclusively presumed that no such jurisdiction has been accepted (R.S. 355, as amended February 1, 1940, 54 Stat. 19; 40 u.s.c. 255).”

You can view a couple of examples of the federal acceptance of a state cession of jurisdiction on this website.  In 1983 the State of Colorado ceded concurrent jurisdiction (link to doc) to the federal government over the following national monuments: (a) Bent’s Old Fort National Historic Site;
(b) Black Canyon of the Gunnison National Park;
(c) Colorado National Monument;
(d) Curecanti National Recreation Area;
(e) Dinosaur National Monument;
(f) Florissant Fossil Beds National Monument;
(g) Great Sand Dunes National Monument;
(h) Hovenweep National Monument;
(i) Yucca House National Monument.

The 1956 Federal GSA Study titled 1956 Part 1 Jurisdiction over Federal Areas within the States is linked here.  Chapter II is titled History and Development of Federal Legislative Jurisdiction, page 11 states the following:  “Exclusive jurisdiction requirement terminated.–There was also enacted, on February 1, 1940, an amendment to section 355 of the Revised Statutes of the United States which eliminated the requirement for State consent to any Federal acquisition of land as a condition precedent to expenditure of Federal funds for construction on such land. The amendment substituted for the previous requirement provided that (1) the obtaining of exclusive jurisdiction in the United States over lands which it acquired was not to be required, (2) the head of a Government agency could file with the governor or other appropriate officer of the State involved a notice of the acceptance of such extent of jurisdiction as he deemed desirable as to any land under his custody, and (3) until such a notice was filed it should be conclusively presumed that no jurisdiction had been accepted by the United States. This amendment ended the 100-year period during which nearly all the land acquired by the United States came under the exclusive legislative jurisdiction of the Federal Government. “

DOJ reference .