He isn't biologically my son but I love him as if he were

So, I'm new here; and I know the title of my question may be confusing but let me explain. I'm a writer, I've been writing nearly full-time for a year now and I am in the midst of writing a story that has an older gentleman who has taken a younger gentleman under his wing as if he were the younger man's son.

Since both are adults, the legality of adoption is not feasible; but as many people experience in life, they bring people into their lives and 'adopt' them anyway as either Aunts, Uncles, Grandparents, or even secondary parents...

My question is: what would be a good word that would describe their relationship? I thought I had a good word for it but for the life of me I cannot seem to get it out past the tip of my tongue.

Solution 1:

You could describe the younger man as the older man's surrogate son.

This is the relevant definition of surrogate (source):

2. A person or animal that acts as a substitute for the social or pastoral role of another, such as a surrogate mother.

Solution 2:

The older gentleman might describe the younger man as

the son I never had

and the younger man might say his mentor is

… a true gentleman and like a second father to me.

For a single word solution

mentor
a person who gives a younger or less experienced person help and advice over a period of time, especially at work or school

Cambridge Dictionaries

Solution 3:

You might say the older man has taken the younger man under his wing.

If you take someone under your wing, you start to protect and take care of them:

Ex: I was a little bit lonely at the time and she took me under her wing.

You could also say the younger man is the protégé or apprentice of the older man, who could be considered his mentor or master.

someone who is helped, taught, or protected by an important or more experienced person

Although you act like both men being adults is a problem, adult adoption isn't entirely unheard of in the world today and historically. In ancient Rome men were adopted to further the line of a given family name and often by emperors to groom their successor. In Japan adults are adopted for similar reasons. For example:

the world’s oldest family business, the Hōshi Ryokan, has been passed down through the family name for 1,300 years

Solution 4:

protégé -- defined by Oxford Dictionaries:

A person who is guided and supported by an older and more experienced or influential person.

‘Ruskin submitted his protégé's name for election’

‘His protégés were placed in important administration jobs; he was on the boards of several start-up companies and advised others about how to deal with the administration'

Origin

Late 18th century: French, literally ‘protected’, past participle of protéger, from Latin protegere ‘cover in front’

A protégé is not necessarily loved as If he were a son, but the connection between mentor (see answer of @Mari-Lou A) and protégé can go as far as the love between father and son.

Solution 5:

fatherly TFD

1. Of, like, or appropriate to a father: fatherly love.