The bombs were discovered today at Heathrow Airport, London City Airport and Waterloo station.
They were described as "A4-sized white postal bags" capable of "igniting an initially small fire when opened".
All of them were marked with a “love stamp” issued by the Republic of Ireland in 2018, showing a red heart and the words “Love” and “Eire”.
They were sent by post from Dublin, the Irish Times reports.
The first package went off at Heathrow Airport offices at 10am this morning.
Nobody was injured in the ensuing small fire but the building was evacuated and anti-terror experts rushed to the scene.
Shortly after 11.30am, a similar device was found in the post room at Waterloo station with the area sealed off.
The third package was received around midday at City Aviation House in the Royal Docks.
Staff were evacuated and bomb squad experts took over.
There were no casualties and Scotland Yard said officers are treating the incidents as linked.
The force said in a statement: "The Met Police Counter Terrorism Command has launched an investigation after three suspicious packages were received at buildings in London today, Tuesday, 5 March.
"The packages - all A4-sized white postal bags containing yellow Jiffy bags - have been assessed by specialist officers to be small improvised explosive devices.
"These devices, at this early stage of the investigation, appear capable of igniting an initially small fire when opened.
"The Met Police Counter Terrorism Command is treating the incidents as a linked series and is keeping an open mind regarding motives."
Mayor of London Sadiq Khan posted on Twitter: "The @metpoliceuk Counter Terrorism Command has launched an investigation after three suspicious packages were found at locations in London.
"Our thanks go to the police, security, transport staff and all involved for their swift actions to keep our city safe."