It is reviving the Paris route after a gap of eight years while the others are brand new.
The Irish budget airline will also start flying between the capital and Cork from December.
The news followed hard on the heels of Spanish airline Vueling announcing new routes with three flights a week between Edinburgh and Paris Orly, and two a week from Glasgow, from November.
Ryanair will operate three flights a week to both Madrid and Paris Beauvais and two a week to Palermo.
The Cork flights will operate three times a week.
Ryanair said the additions would increase its routes from Edinburgh this winter to 50, after flying 58 routes from the capital this summer.
They follow winter flights to Shannon, Knock, Tallinn and Turin being added this year.
However, aviation trackers said Ryanair had removed its Edinburgh to Girona, Valencia, Baden-Baden/Karlsruhe, Luxembourg, Stockholm and Weeze routes.
The airline has yet to confirm the changes.
Edinburgh Airport aviation director Kate Sherry said: “We know people need and want to travel, and with restrictions easing, we want to provide as many options as possible for them to finally take that trip they’ve been waiting for.
"It’s clear to see there is confidence in the Edinburgh market as one for sustainable growth and it is good news that Ryanair are working with us to add new routes where possible."
Ryanair director of marketing Dara Brady said: “We remain committed to re-building Scotland’s tourism industry and strengthening connectivity as Ryanair continues to grow in Europe and travel returns to pre-pandemic level."
But he warned: “While Ryanair is committed to Scotland and Edinburgh airport, the lack of government support continues to create further barriers to boosting traffic and growth.”
However, Ryanair told The Scotsman in July it was in talks with airport chiefs to increase its eight aircraft based in Edinburgh.
Director of commercial Jason McGuinness said: "We are currently in discussions with Gordon [Dewar – Edinburgh Airport chief executive] and his team, which are progressing very well.
"We would certainly hope to be adding new aircraft at Edinburgh over the coming years.”