Uploading to S3 from EC2 instance fails due to denial of access

I am trying to copy a file into an S3 bucket of mine:

aws s3 cp file.txt s3://my-bucket-34123

But I get:

upload failed: ./file.txt to s3://my-bucket-34123/file.txt 
A client error (AccessDenied) occurred when calling the PutObject
operation: Access Denied

I created a user "EC2" added the policy "AmazonS3FullAccess" and configured the credentials via aws configure.

Uploading to the bucket from my PC does work as usual.

Any ideas what might be wrong or how to troubleshoot?