Updated 13th February 2019 for Make Tax Digital (MTD) compliance - Read more about MTD

Integrate via Sage Pay (now Opayo)

It has been possible since April 2016 to integrate with Sage50 Invoicing via Sagepay, their payment processor. This will be a simple way to integrate into their accounts package if you are only taking payments via SagePay (which also offers processing for Paypal account holders).

Read more on Sage's website

Accounting System Integration For Invoices Using Tradebox (Sage/Xero/Quickbooks)

If you use multiple or different payment processors then you can send order information from your system via the Tradebox integration service to Sage 50 , Sage One, Xero Accounts & Quickbooks to create invoices, eliminate duplicate keying and comply with MTD requirements from 1st April 2019 onwards. 
Read more about Tradebox integration for Sage

Integration Into Xero & Quickbooks Via Unleashed

Unleashed is an inventory management system for manufacturers, wholesalers and distributors offering real-time inventory control and reporting which integrates into Xero accounting and Quickbooks (not Sage which is a competitor) plus Amazon. Read more about Unleashed & Xero integration.