Paragraph 14 of Schedule 7 to the European Union (Withdrawal) Act 2018 originally stated that:
A statutory instrument containing regulations under section 20(4) may not be made unless a draft of the instrument has been laid before, and approved by a resolution of, each House of Parliament.
...where section 20(4) allows the government to issue an SI to change exit day to match any extension agreed by the EU and UK. This paragraph required both Houses to approve the SI before it comes into force, and is known as the affirmative resolution procedure. (See also this related question.)
However, section 2 of the European Union (Withdrawal) Act 2019 amended this to read:
A statutory instrument containing regulations under section 20(4) is subject to annulment in pursuance of a resolution of either House of Parliament.
This is the standard wording which means that the government can issue an SI to come into force whenever it likes, but either House can revoke it within 40 days. This is known as the negative resolution procedure, and makes it easier for the government to make changes it needs without having to wait for Parliament to approve them (though it should be noted that it's extremely rare for Parliament to block or revoke SIs).
With that change in place, the government issued The European Union (Withdrawal) Act 2018 (Exit Day) (Amendment) (No. 2) Regulations 2019, which changes the definition of exit day to 31 October 2019 at 11.00 p.m. The SI came into force at 3:15pm on 11 April 2019, and was laid before Parliament an hour later.
It appears in the Votes and Proceedings of the House of Commons for that day, in the list of "Papers subject to Negative Resolution".
Summary: Parliament no longer needs to approve the new exit day, but it has a fixed amount of time in which it can reject it.