Under Article 2 EU Data Protection Directive it defines that personal data;
shall mean any information relating to an identified or identifiable natural person ('data subject'); an identifiable person is one who can be identified, directly or indirectly, in particular by reference to an identification number or to one or more factors specific to his physical, physiological, mental, economic, cultural or social identity;
It also states that;
'processing of personal data' ('processing') shall mean any operation or set of operations which is performed upon personal data, whether or not by automatic means, such as collection, recording, organization, storage, adaptation or alteration, retrieval, consultation, use, disclosure by transmission, dissemination or otherwise making available, alignment or combination, blocking, erasure or destruction;
But under Article 7 it states that;
Member States shall provide that personal data may be processed only
(a) the data subject has unambiguously given his consent; ...
So from what I understand of this, you should be ok so long as you have a legal notices or terms and conditions of using the app stating that you will be storing this information.
This directive is also being extended so that US companies may also process your user information in the future. Extended EU Directive