Farooq Shah, 21, of Station Road, Forest Gate, east London, stabbed Mariana Popa to death in Ilford Lane, Redbridge, on 28 October.
Shah was ordered to serve a minimum of 28 years for the murder and received a concurrent six year sentence for robbery.
The Met Police said he had "deprived a young daughter of her mother".
Ms Popa, a Romanian national, had arrived in the UK only weeks before her murder, police said.
She had a six-year-old daughter and  was in the early stages of pregnancy at the time of her death, officers said.
On 28 October police patrolling the area said they spoke to her three times and issued her with a caution for soliciting.
CCTV footage showed Ms Popa walking along with Shah and his bicycle shortly before 00:00 BST, before he took a knife from his back pocket and stabbed her in the chest.
Shah made off on his bike, while Ms Popa ran to a nearby shop where she collapsed. She was taken to an east London hospital where she died shortly afterwards.
The post-mortem examination found the 24-year-old died from shock and haemorrhage and stab wounds to the chest.
About 400 hours of CCTV footage was reviewed during the investigation and officers were able to identify the bicycle used by Shah during the attack and track his movements to an area around St Francis Way.
During door-to-door enquiries on 6 November the bike was discovered in the area and Shah was arrested inside a flat by police.
A mobile phone was also found at the flat and officers discovered that less than an hour before the killing Shah robbed a partially sighted man in his 50s in Harold Road, Upton Park.
The victim was able to describe his robber's distinctive thick beard, police said.
Det Insp Darren Richards, from the Met Police, said: "Shah has never given any reason or expressed any remorse for killing Mariana.
"Fortunately he was caught on camera and we were able to put together his movements and bring him before the courts.
"His callous murder has deprived a young daughter of her mother and a family of their loved one.
"I hope today's sentence brings some sense of justice for them."
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