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Peribit is a specialist in optimising wide area networks, and Redline is a pioneer in front-end server optimisation, including the speeding up of website response times.
The Peribit acquisition is valued at £187m, and the Redline deal is worth £69m.
Commenting on the move, Gartner analysts Mark Fabbi and Joe Skorupa said, "All network managers looking at upgrades to their router, VPN or Wan architectures must include Juniper on their shortlist of suppliers.
"Considering only one provider for your Wan infrastructure is no longer an acceptable approach. Likewise, network and application architects looking to improve datacentre infrastructure or application performance should consider Juniper's new offerings."
Business demand for application acceleration products has increased dramatically in the past two years, said Gartner.
Juniper chief executive Scott Kriens said, "The addition of these application acceleration technologies to Juniper's routing and security solutions is a natural extension of our traffic processing strategy.
"We are raising the bar on what users can and should expect from the network."
Peribit's products enable applications to run more efficiently over a Wan, and more than 900 large companies worldwide have installed its products.
Redline designs network products that maximise the performance, flexibility and scalability of web-enabled enterprise datacentres and public websites. Redline has more than 350 enterprise customers.