You can't directly add VF Component..
But you can add a VF page in Home Page layout
Create a Visualforce Page and add your component.
<apex:page showheader="false" >
Step 2: From Setup, click Customize | Home | Home Page Components.
Step 3: Click New.
Step 4: Enter a name for the component ...
You can not override entire Home tab by the visualforce page.
Though, you can create home page component and use your visualforce in the component and finally add the component into this homepage.
Otherwise create a custom visualforce tab and rename that tab as 'Home` and use this in your app.
Navigate to your App and select the Default Landing tab.
Looks like there is an option but available only in Winter'18 release.
You need to create the following component HomePageSingleColumnTemplate with the following code
<aura:attribute name="main" type="Aura.Component" />
At this time, customers are only able to put up to three dashboards components on their Homepage at a time.
As a workaround customers can customize their Homepage by selecting a different dashboards to display on their Homepage via the following click path: Name > Setup > My Personal Information > Change My Display.
However, if the customer would like to ...
You may add the VF page as a section of the home page [a bit like inline VF].
Here are the steps to follow :
You should create a Home Page Component.
Setup > Customize > Home > Home Page Component
You must create New under Custom Components.
Then you may create a new layout for your home page.
Setup > Customize > Home > Home Page Layouts > New
Your approach will not work.Try building dashboard with analytics:reportchart and embed this page in visuaforce homecomponent
<analytics:reportChart reportId="00O55000000OZVL" />
You can do the next steps
Create a visualforce.
Create a app and set default page is the visualforce.
Duplicate a Profile for that user and in the profile configurate that only can access to the new visualforce
You can try this approach. Try creating a report on leads whose lastmodidifeddate > 90days. Have a dashboard of that report with the count of records. Place this dashboard on the homepage then.