With respect, it doesn't make much sense to have the ENTIRE bib entry link to the DOI page, since, an individual bibliography record may have BOTH URL and DOI's, either, or neither.
I use the following command, along with the hyperref package, which gives a blue colored hyperlink to the DOI webpage for the bibliography entries that have DOI records.
In the preamble, put the following:
\usepackage[hidelinks]{hyperref} %boxes hidden, remove hidelinks if boxes are desired.
Then before the bibliography is called:
\def\mybibdoicolor{\color{blue!75!black}} %change color to suit.
\newcommand*{\doi}[1]{\href{http://dx.doi.org/\detokenize{#1} {\raggedright\mybibdoicolor{DOI: \detokenize{#1}}}}
Finally, the bibliography can be called:
\bibliography{BIBDATAFILE}
An exerpt from my output is displayed below, noting the blue DOI record/s held in references [41-43], each can be clicked from inside PDF, in such event, the user would be redirected to the relevant site. In this case, as an example, should the user click on the DOI record inside [41], he/she would be redirected to http://dx.doi.org/10.1098/rspa.1925.0147, which in turn redirects the user to the publication.

biblatex
? You can activate the display of dois for each entry (if available) withdoi=true
. Then you can click on the doi information in a bib entry to open the web site. Why must it be the title?biblatex
then this question is relevant. Some of the answers apply to nonnatbib
styles.