Mr Johnson said Mrs May will be making a statement in the House of Commons on Monday and it will give parliamentarians a chance to hold the executive to account.
In the biggest foreign military action so far against Syria's regime, Western officials said a barrage of cruise and air-to-land missiles hit targets near Damascus and in Homs province including a scientific research centre, storage facilities and a command post.
"We are prepared to sustain this response until the Syrian regime stops its use of prohibited chemical agents", the United States president said in a televised address.
"Important infrastructure was destroyed which will result in a setback for the Syrian regime", Mattis said.
"We have sought to use every possible diplomatic channel to achieve this", the prime minister said.
"This collective action sends a clear message that the worldwide community will not stand by and tolerate the use of chemical weapons", May said at a press conference, calling the military action "right and legal".
Britain has blamed Russian Federation for the poisoning - a charge vehemently denied by Moscow which has accused London of failing to come up with evidence for its claims.
In her comments, May also alluded to a nerve agent attack in Britain last month on a former Russian spy and his daughter.
Mom who drove SUV with family off cliff was drunk
Authorities are also continuing to search for members of another family farther south along the Mendocino County coast. They used an underwater probe to see if the vehicle or anything metallic could be located.
"I have done so because I judge this action to be in Britain's national interest", she added.
Opposition Labour leader Jeremy Corbyn had said Britain should press for an independent United Nations -led investigation into the suspected chemical attack in Douma rather than wait for instructions from Trump on how to proceed.
Prime Minister Justin Trudeau said in a statement that Canada stands with its allies and that it supports the decision " to take action to degrade the Assad regime's ability to launch chemical weapons attacks against its own people".
For his part, the leader of the UK Independence Party (UKIP), Gerard Batten, opposed the British military action in Syria.
The DUP has backed Prime Minister Theresa May's decision to authorise air strikes in Syria. "The opposition does not operate helicopters or use barrel bombs".
"Where is the legal basis for this?" he said.
Over 100 missiles were fired on the morning of Saturday, April 14, targeting what representatives of coalition forces called chemical weapons sites in retaliation for an earlier poison gas attack.