How to add 'Upload' functionality to custom fields?

I’ve created some custom fields that should contain links to images. So currently to add an image I have to do the following:

1. Open up media library
2. Upload images
3. Save links
4. Go to posts > add new
5. Create some posts
6. Paste links to images to custom fields

I want it to be like:
1. Go to posts > add new
2. Click “Upload” button next to each custom field and I want it to paste link automatically

Is there any WP function that allows me to handle uploads that way? If not, how would I do that?