What is the economic solution to mass immigration?

I've heard countless stories about mass immigration to countries, and the question that I'm sure many of you have is, what is the economic solution to this? We want immigrants to come in and legalise their entry, but not just because it's illegal. In a labour market, legal migrants can assimilate and enter the economy without any restrictions like under-the-table workers. Having illegal immigrants is a huge burden to the economy.