Sajid Javid told MPs, according to the BCC, the same policy would also apply to anyone under the age of 18 from that date.
The government would give more details this week on self-isolation rules for international travel, he added.
"If someone gets their second dose just before or just after 16 August, they'll need to wait two weeks, after which their second jab can take effect and give them these new freedoms," Secretary Javid said.
As under-18s are not routinely jabbed, he said a similar exemption from self-isolation rules would be extended to them.
He said adults who had been in close contact with a positive case would be "advised" to get a PCR test as soon as possible to make sure they hadn't been infected, while for children it would be dependent on their age.
People identified as close contacts of a confirmed Covid case are currently required to selfisolate for up to 10 full days when contacted by NHS Test and Trace.
He added that "of course" anyone that tested positive would have to self-isolate whether they have had the jab or not.
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