There are services that do that, but I wouldn't trust any of them now-a-days. Tons of applications that offer "free" transfer options, but do you want to give access to any/all personal info on your computer? (hint: answer should be "NO").
Microsoft doesn't have the Windows Easy Transfer tool supporting Windows 10, but they did partner with a company to offer a paid application to move files from one PC to another: (
link in this page at Microsoft). Personally, I'd just use a large USB to do this and not pay for an app that basically does the same thing.
Sounds like you want a lot for free (especially transferring 'a few gigs')... you're best off doing what most others do and transfer your files to an outside drive or USB, then move them to the new computer. You will have to reinstall any programs on the new PC manually (which is standard). Just make a list of the programs you have installed and reinstall from their official sites on the new PC.
This thread at MS has a good explanation as to why you can't do this and how to reinstall those programs manually.
Good luck!