What you're feeling is a relatively common psychological phenomenon called Imposter syndrome.
Impostor syndrome is a psychological phenomenon in which people are unable to internalize their accomplishments. Despite external evidence of their competence, those with the syndrome remain convinced that they are frauds and do not deserve the success they have achieved. Proof of success is dismissed as luck, timing, or as a result of deceiving others into thinking they are more intelligent and competent than they believe themselves to be.
Psychological research done in the early 1980s estimated that two out of five successful people consider themselves frauds and other studies have found that 70 percent of all people feel like impostors at one time or another. It is not considered a psychological disorder.
I too am a developer who struggles with receiving praise. It was a great relief to me just to know that other people, even people wildly more successful than I, commonly feel inadequate in the face of praise. At the end of the day, I try to remember that my employer is the one paying the bills; if they're happy with your work, that's all that really matters.
In a broader sense, you'll be a much happier and successful professional if you learn to take all feedback at the sincere face value. I'm not saying that everyone you encounter in the workplace (or in life) is sincere and wholesome, but undervaluing your contributions will not help you recognize or cope with adversarial personalities. On the contrary, if you don't internalize your accomplishments and respond to feedback (both positive and negative), it will harm your professional relationships and your job satisfaction.
Edit to clearly say that the other answers are wholly correct that you are deserving of the praise you're receiving. Just because (nearly) everyone feels that way from time to time at all levels of professional achievement doesn't mean they're right. Besides, whose opinion would you believe: the consensus of the experienced team members, bosses and company owner or the lone new guy? You might be tempted to chalk that up as an argument from authority, but consider that the people whose job it is to evaluate your work are all in agreement that you are doing well. That's not as strong as a scientific consensus, but you can't dismiss it either.
In this sense, your boss (manager, project lead, CEO, etc.) is your customer: your employer pays you a salary in exchange for your work. As we know about customers, they're always (usually, mostly) right. This cuts both ways: if you ever receive what you feel to be undeservedly negative feedback, you need to react to it with sincerity and professionalism as well.
If you can't overcome your sense of under-accomplishment through willpower, then consider drawing upon it to drive your own productivity. Set for yourself what you consider to be a truly difficult goal. This can be a professional milestone, but you might want to start out with a simple, task related incremental improvement. If you weren't satisfied with your last project, set aside an hour in a work day or free time to quantify how you think it could be improved, translate that into individual tasks, and come up with a realistic estimate of effort required. (Note that these steps are difficult skills to master in and of themselves, so even just taking it this far will improve your value as an employee.)
Once you have a plan, consider how realistic your expectations are. Would it take a truly enormous amount of effort to improve upon what you've done? Stop there and reflect upon what you've already accomplished and try to take to heart the praise of others. Is this a series of minor, incremental improvements that you're interested in doing for building your own skills or easing the future workload? Consider making it official and turning your personal goals into your work goals. If your project goals provide real value to the company, they may prioritize it over another project and assign more resources to it, in which case you've just contributed technical leadership and ownership, both very valuable resources to any team.
Then set about your task. Continue to push yourself until you've accomplished the improvement. Keep a realistic perspective and remember that you're going the extra mile so you don't get discouraged. It may take longer than you think, it may be harder than you think, you may have extreme difficulty tackling a side project and staying on top of your regular work. If you aren't making the kind of progress you expect, step back and reevaluate your estimates both for accuracy and realism with regard to your other responsibilities.
In any case, whenever you make progress on your own goals, take a moment to reflect that you really have accomplished something you yourself thought was difficult and worthwhile. That should put your mind at rest that your accomplishments are noteworthy and you are deserving of praise.
Note that it is possible to take this drive too far. If your mood or job performance start being impacted negatively, then you may be working yourself too hard. Low self esteem can be a serious and chronic condition; with regard to a career, it can drive some people to workaholism and depression.
Everyone (...) has a feeling of inferiority. But the feeling of inferiority is not a disease; it is rather a stimulant to healthy, normal striving and development. It becomes a pathological condition only when the sense of inadequacy overwhelms the individual and, far from stimulating him to useful activity, makes him depressed and incapable of development.
Alfred W. Adler, MD and Psychotherapist in The Science of Living
