From next summer the airline will carry three million passengers and sustain 3,000 jobs with the additional flights, chief executive Michael O'Leary claimed.
The new routes will be from Edinburgh to both Bologna and Cagliari in Italy, Beziers in France, Santander in Spain, the Greek island of Corfu and Katowice in Poland, and from Prestwick to both Rzeszow and Warsaw in Poland.
Mr O'Leary said they will start in around six months, while nine other flights from the airports will increase in frequency.
The new routes from Edinburgh Airport are significant because Ryanair reduced its flights from there in February after failing to agree lower costs and charges with operator BAA.
The airport is now run by Global Infrastructure Partners (GIP) and Mr O'Leary said further announcements on growth are likely.
"We have eight new routes out of Glasgow and Edinburgh for summer 2013, growing both airports by around 400,000 passengers that should lead to 400 new jobs spread evenly between the airports.
"We've been very impressed by GIP. They are very committed to growth and we've been negotiating now for a couple of months. I don't think today's announcement will be the last because, given their commitment, they want to grow the airport quickly and that's a breath of fresh air after dealing with BAA who only wanted to fatten profits for its eventual sale."
Mr O'Leary backed calls from all of Scotland's main airports for the UK government to scrap air passenger duty. Last month Aberdeen, Glasgow and Edinburgh airports commissioned a report that claimed the charge could lead to a drop in both passengers and tourism spending.
The tax could cost the Scottish economy £210 million a year in lost tourism spending by 2016 and could lead to 2.1 million fewer passengers in Scotland's airports by then, the report claimed.
The majority of MSPs believe the Scottish Parliament should have control over the aviation tax.
Its rate depends on a passenger's final destination. There are four bands based on the distance between London and the capital city of the destination country, ranging from £13 to £184.
Mr O'Leary said: "I think APD (air passenger duty) has done huge damage to Scottish tourism and Scottish jobs. The problem is it has really hit the domestic routes.
"We used to carry about 300,000 passengers a year between London and Prestwick but we closed that route because you can't fly passengers at £10 when the Government is taking £13 in tax. So I think it's important for Scotland that APD is scrapped, particularly for domestic routes.
"In Northern Ireland APD has been scrapped for transatlantic flights and there are campaigns to remove it from domestic flights now. So there is a grave danger that Scotland will get left behind.
"It's very important Scotland gets control of that tax and whether they get independence or not, the Government needs to reverse or scrap it."
Gordon Dewar, chief executive of Edinburgh Airport, said: "The whole purpose of Edinburgh Airport is to connect Scotland to the rest of the world and we do that by working with the airlines that offer the biggest choice of routes and carriers.
"So when an airline the size of Ryanair isn't getting on with the airport, that isn't good for anyone and changing that was one of the focuses since GIP bought the airport. And today marks the successful re-establishment of a good relationship and the fruits of that labour are the new destinations and increased passenger numbers."
Mr Dewar added his voice to the criticism of APD.
"The whole industry is together on APD. We are by far the most expensive in Europe. Put in context, APD charges for a passenger are larger than airport charges for the same journey. That doesn't make sense to me and if you consider Scotland as the north-west periphery of Europe, it doesn't seem to make sense to make it difficult and expensive to get here."
Prestwick Airport has been up for sale since March and it is hoped the expansion by Ryanair will interest potential buyers.
Tom Wilson, chief executive of Infratil Airports Europe, owners of Glasgow Prestwick, said: "This expansion is good news. Despite tough economic times and ridiculously high levels of APD, we are actually seeing passenger numbers rise and it's good for the business and for Ayrshire and Scotland.
"The relationship between the airport and Ryanair is very important for both parties, as well as the jobs that can come from today's announcement there are also another 300-400 in Ryanair's maintenance base in Prestwick."
Mr Wilson said discussion with interested parties are ongoing.
Mr O'Leary said: "I think Prestwick is growing again and has a viable future. We have an unbreakable commitment to Prestwick. We have two large hangars and we employ over 500 engineers but people wanted to see a public demonstration of our commitment and the best way to do that is the announcement of new routes and growing traffic through that."