The father-of-two, 34, was pursuing a stolen Ford Focus car when it mounted the pavement and hit child actor Makayah and Rozanne Cooper, 34, in Penge, south-east London on August 31, 2016.
A second child, who was aged 10 at the time, was also seriously injured, the Old Bailey heard during the trial.
The court heard how during the six-minute chase through residential and one-way streets, PC Welch’s police BMW car reached speeds of more than 60mph.
It heard the vehicle that was being chased was driven by a 19-year-old man called Joshua Dobby.
He lost control of the car on Lennard Road, crashing into a bollard and crushing the three victims.
Dobby was later convicted of two counts of manslaughter by gross negligence and one count of causing serious injury by dangerous driving.
PC Welch, from Chatham, Kent, denied two charges of causing death by dangerous driving, one count of causing serious injury by dangerous driving, and an alternative charge of dangerous driving.
The married father-of-two told jurors that he joined the Metropolitan Police at the age of 20 and underwent training in advanced driving.
He told the court he had been in five pursuits of up to an hour in length before the fatal incident.
He said: “I have always wanted to be a police officer. It was my dream as a child. It’s all I’ve ever wanted to do.
“I just wanted to help people. That is what police do – stop bad coming into the world, helping people.”
On August 31, 2016, Mr Welch said he was notified that a lost or stolen Ford Focus had activated an ANPR camera on Penge High Street.
He responded with blue lights and sirens as he searched the local area including “crime hotspots” but did not locate the vehicle.
At about 2pm, he spotted it while he and his colleague were responding to a road traffic collision.
He told jurors: “There was traffic in front of us in Avenue Road, so I activated my blue lights and sirens to safely facilitate myself through the traffic towards the subject vehicle.
“I can categorically say he was driving at excess speed on Mackenzie Road.”
Asked what the aim of having lights and sirens on were, he said: “Alerting members of the public, pedestrians, and other road users of what’s going on.
“It’s a clear audible sign you have got a marked police vehicle behind and to stop.”
He said he had been made aware the vehicle he was pursuing was involved in the theft of fuel, but not about an earlier pursuit five days before in Kent.
The jury heard how PC Welch had assessed the risk at one point during the pursuit as “low”.
However, the prosecution alleged that on “any sensible analysis, the risk posed by the pursuit, taking account of the driving of both vehicles, was at a higher level of risk”.
When asked to explain his assessment at the time, Mr Welch said his “visibility was good” and the road he was on was straight.
A jury deliberated for half a day to find him not guilty of the charges against him.
PC Welch thanked jurors as he left the dock after he was cleared.
Following the verdict, the Met said it will now consider misconduct proceedings against both PC Welch, who is currently on restricted duties, and a former officer who was also involved in the pursuit, but has since resigned.
No criminal charges were brought against the colleague. He was a passenger in the car and in contact with the police control room during the pursuit.
The Met’s South Area Commander Chief Superintendent David Stringer said on Thursday: “The deaths of Rozanne Cooper and her 10-year-old nephew Makayah McDermott have naturally left their families devastated.
“Our thoughts remain with them and we offer everyone affected by this terrible incident our sincere condolences.
“Police pursuits must be carried out in very careful and controlled circumstances in line with policy to ensure they do not put anyone at risk. The jury has found PC Welch did not commit a criminal offence but misconduct matters will now be carefully considered.”