The supermarket giant said it will start the same-day service at three stores, before rolling it out to 30 stores by Christmas, to keep pace with a rise in online orders across London.
It said the service will allow customers who order by 12pm to have their shopping delivered to their home by 6pm, or they can use its click and collect service to pick it up from a supermarket at 4pm.
The move is being underpinned by the launch of a new online fulfilment centre in Bromley-by-Bow, east London, where it plans to immediately recruit 470 people followed by a further 430 by 2020.
The announcement comes after Amazon revealed its push into the UK grocery market in June when it launched AmazonFresh, which offers same-day fresh food deliveries to 128 London postcodes.
Robbie Feather, Sainsbury's director for online, said: "Demand for our online delivery service in the capital continues to grow.
"We expect this trend to continue as more and more customers enjoy the flexibility of multi-channel shopping using our groceries website and app, in addition to visiting stores.
"Our online orders are currently picked from supermarket stores across the UK and this model will continue, but the Bromley-by-Bow centre will help us keep pace with demand in London, enabling us to fulfil another 25,000 orders per week."
Sainsbury's said the 185,000 sq ft online fulfilment centre will be opened in the autumn and has been kitted out with the latest automation and picking technology.
The jobs created at the site will range from drivers and order pickers to product replenishers and managers.
The three stores taking part in the same-day delivery trial include the Sainsbury's at Streatham Common, Richmond and Brookwood in Surrey.
It said the trial service will be " competitively priced" for customers and free on orders over £100 delivered between Monday and Thursday. Customers who have a Sainsbury's "delivery pass" will not be charged.
The retailer previously announced that it was planning to double its click and collect grocery sites to 200 by the end of the next financial year.
Feather added: "As our online sales grow we are seeing an increasing proportion of orders placed for next day delivery, so this trial is a natural next step in delivering our strategy to help customers shop whenever and wherever they want."
Britain's second-largest supermarket reported a 0.8% drop in like-for-like sales excluding fuel for the 12 weeks to June 4.
The fall marked a setback after a return to quarterly like-for-like growth for the first time in more than two years the previous three months, when sales edged 0.1% higher.
The grocer is currently waiting to hear if the Competition and Markets Authority (CMA) will launch an inquiry into its £1.4 billion takeover of Argos owner Home Retail Group.
The CMA said it would consider comments on the deal and announce its decision by July 25.
The British grocery sector continues to be locked in a supermarket price war, which has seen the Big Four supermarkets slash their prices to protect market share from the rise of German discounters Aldi and Lidl.
Our BQ Bulletin emails will land in your inbox at 7.30am, Monday to Friday, with a mix of the latest local business news, national news, and features to inspire you. Sign up here!
Click here to read our privacy statement